Interesting request...
What is your definition of weird? Rare and hard to find? Peculiar flowers? Patterned leaves? Or do you mean tropical-like plants for colder zones?

I will just guess on what weird means and start suggesting some things...
Vancuveria hexandra- Inside Out Flower. Its a native and related to Epimedium. The flowers look like they are growing at the wrong end.
Tomiea menziesii- Piggy Back Plant. Not showy but a good ground cover. It has brown flowers and little plants will form on the stem.
Chyptotaenia japonica 'Atropurpurea'- Japanese Ornamental Parsley. It has pretty purple leaves with nondescript flowers. What is really interesting about it is the stems. They look like bare tree branches.
Asplenium scolopendrium- Harts tounge Fern. It looks like a Birds Nest fern but is amazingly hardy.
Athyrium filis-femina 'Frizelliae'- Tatting Fern.
Bletilla striata- hardy ground orchid.
Dictamnus- Gas Plant. Its dried pods are flamable!
Geum trifoliata 'Prairie Smoke'- Old Man's Wiskers. Fuzzy seedheads
I have more, but im not sure what ive listed is what you consider weird.
CMK

CMK

You are right on track! Thanks for the suggestions!

We live in an unusual home and I'd like a garden to match! The odder the better!

Of course, I have to get it to grow in our cool, damp zone 5. I do not mind container plants.

I will go look up these and would LOVE MORE !!

Leasa

Friends who visit love the look of this one, it is a Plume Poppy. It really has a tropical look but is hardy.

The bees LOVE it! It is very tall, I'm guessing at least 10 feet and the leaves are huge--for anything around here!

Im glad thats what you were looking for. I grow all of the plants I mentioned above, and we get very cold wet winters and springs.
Here are a couple more:
Thalictrum is similar to your Plume Poppy. My T. rochebrunianum gets about eight feet tall with sprays of purple-pink flowrs. The stems look like celery (to my eyes anyway). Thalictrum flavum-glaucum has sulfur yellow puffs of flowers that smell so sweet.
Crocosmia- Upright strappy foliage with brightly colored flowers (comes in reds, oranges, yellows). I love how tropical it looks.
Corydalis. The foliage is ferny and the flowers look like guppies! I have the yellow C. lutea and amazing bright blue C. elata. Reseeds really well.
Also, black leafed perennial geraniums. So unusual! Many cultivars available
Astrantia- Masterwort. Has peculiar, but pretty, looking flowers.
Hypericum 'Albury Purple'- St. Johns Wort. Purple tinged leaves. Amazing yellow flowers followed by reddish berries that turn black!
Kirengeshoma- Yellow Wax Bells. The foliage is large and looks like Maple Leaves. The flowers are yellow and waxy. The buds take MONTHS to open. They look like little acorns before fully opening.
Polygonatum- Solomon's Seal. Has little white bells with green edging.
Primula vialii- Poker Primrose. Looks like a hot poker! Red and purple flowers.
Oreganum rotundifolium 'Kent Beauty'. Flowers look like little cones!
Lonicera sempervirens- Trumpet Honeysuckle. Hummingbirds love it and it looks tropical.
Rudbeckia occidentalis 'Black Beauty' and 'Green Wizard'. Looks like regular Rudbeckia but without petals.
Tricyrtis- Toad Lily. Has tropical like flowers that are spotted!
Dont forget Spiderwort (Tradescantia).

There are just so many more. Here are some mags I like to look at because they have such unusual plants:
Plant Delights Nursery
Heronswood Nursery

Make sure to show us your cooky garden when its completed! ;-) Hope this helps you.
CMK

Not that I am any kind of expert - but this is kinda wierd!!!

Here is a link that might be useful: Eye balls

Don't forget the Eyeball plant Spilanthes oreracea, hope I spelled that correctly. It was mentioned here in the last day or two. I just had to look that one up :o).

Annette

Dang, I meant to type oleracea. A

I love the Amaranth or Love Lies Bleeding. It is an annual like the Spilanthes above and very unusual looking. I grew one for the first time this year, and I love it!

allium christophii is a short and very large spiky ball, that always gets lots of comments.

clematis tangutica is a yellow clematis that gets many wispy seedheads that look like beards

if you have room for a trellis, snake gourds are a real conversation piece

Oh Goodie! You folks are wonderful! I'm so looking forward to this fun filled garden!

CMK thanks for the catalog tips!

This will be a fun, fun, fun garden to plan, grow and show!

Leasa

Someone posted easter egg plant recently. I found this old post with pictures. It is a little squash and cute.

Squirrel girl

Here is a link that might be useful: Easter egg plant

Some of the euphorbias are rather unusual looking. I think it is polychroma that is electric yellow--put it with black foliage plants or bright purple or electric blue blooms?

I can't wait to see what you do with this "wild and weird" garden! Too much fun! LOL

Cameron

Here's what weird annuals are in my Minnesota garden right now:

Leonotis (looks like a Dr. Suess plant)

Cyperus papyrus (does NOT need to be in or near a pond!)

Cuphea 'Caribbean Sunset' (like tiny orange tubular fish with faces)

if you don't mind poisonous, the castor bean 'Zanzibar' makes an 8 foot tree in one short summer

how about a giant black Colocasia like 'Black Ruffles'

Mina lobata (a vine)

Cardiospermum (common name is Love-in-a-puff)

I'll try to think of some others!

Do you want more suggestions?
I dont grow these next plants personally...

A tropical looking grass, Miscanthus sinensis 'Giganteus'. I saw it at a local park and it is SO COOL! The foliage is dark green and strappy. The plant is very erect and was twelve feet tall, and it hadnt even put on plumes yet!
Tree peonies have a tropical feel...
Litium lancifolium-Tiger Lity. Bright orange with black spots.
Darmera peltata-Umbrella Plant. Large roundish leaves with pearly red flowers.
Astilboides Tabularis. Similar to above plant but with larger leaves. Looks like it could have been around with the dinasours...
Asarum- Wild Ginger. Groundcover with the strangest little flowers you ever saw. Does well in dry shade.
Arisamea- Jack in the Pulpit. You hae got to see it for yourslf. Its just too hard to describe.
Angelica gigas- Angelica.
CMK

I asked my dh if I have anything weird growing, and he thought of my Centauria Macrocephala. When I bought the plant the tag also called it a yellow perennial bachelor button. When it first started to bloom, it was gold balls, about an inch in diameter. They stayed that way for a number of days, and I wondered if they had been tagged wrong. They really were weird looking. Then, even weirder, yellow puffs appeared on top of the gold balls, and over a couple days, filled out, and we called the flowers yellow fluff.

Oh, I just remembered someone here had shown a photo of a pretty centauria that was a pink/lavender color! I just googled the name I gave you above, and looked at images, and found a number of plants you may like to try.

Moonflowers, and daturas of different kinds are unusual, too, but poisonous.

Sue

I kept thinking, 'Is anybody going to mention 'Harry Lauder's Walking Stick'? I didn't see Harry show up. I've never even seen one, but it looks weird in pictures.

Nell

Nell, Harry looks great naked :o) but when all dressed up in his seasonal greenery to me he looks a little peaked. A

Hi Leasa, A really unusual plant is Canna "Phaison". It has beautiful foliage with an orange flower. The nursery described it as the Howard Stern of plants. I'm not sure if it is hardy to your zone though. Nikki

Thanks so much for all the WONDERFUL suggestions!

My computer died in PA and I'm sad to say the least. After all day trying I got it alive enough to get back ups of the files that were not already backed up and the photos of our fixer.

the good news is my hubby has this lap top that he never uses and it is wi-fi ready and I bought a wireless modem that I was waiting for a free minute to install and now it is done!

I still have to see it it will work in the kitchen...

Thanks everyone so much for the suggestions,it will be a real fun garden to make and enjoy!

Leasa

I came across this bulb that looks pretty weird to me in the pictures that might be of interest and is something you can plant now: Snake's Head Iris

Here's a link to information and pictures.

Here is a link that might be useful: Snake's Head Iris

I grew 'Harry Lauder's Walking Stick' for years in a shallow cement tub,so it never grew real tall. But it did look wierd when all the leaves had fallen off. I also grew Dutchmans Pipe,( Aristolochia elegans). It looks like little ducthmans pipes.

Sue

I just remembered another, Syneilesis aconitifolia (Shredded Umbrella Plant) it's one that is a little different. A

Hermodactylus tuberosus, Snake's Head Iris, is not really weird, it just has a weird name. I planted some; they're quite pretty but an odd color that needs good companions.

Nell

The blackberry lily (Belamcanda chinensis) has pretty little flowers, but very interesting seed heads that look just like--wait for it-- blackberries! The candy lily (Pardancanda norissii) is a cross of the blackberry lily, and its seeds do the same thing. The seed looks juicy and edible.

Pat

Leasa, Edna grows a type of asclepias whose name I can't quite recall that is indeed weird. Let's just say it resembles male genitalia? I don't think you can get weirder than that... Maybe she'll chime in to add more info or someone else remembers the name. Something like Family Jewels? Anyone?

Eduarda

Found it! See the link below. It says zones 7-10, so you're out of the hardiness zone, but maybe in a protected spot, or as an annual? Can't get weirder than that!

Eduarda

Here is a link that might be useful: Family Jewels

Y'all do know about that little hot pepper that would go perfectly with the Asclepias 'Family Jewels' that Eduarda mentioned -- Capsicum annuum var. annuum 'Peter'?

You guys are a hoot!

I have seeds if you want some. It was suppose to reach 4-5 feet..well, it's way over 8 or 9 feet and still growing. The balls are soft and fuzzy. Quite a conversation piece *lol* Monarchs use it as a host plant.

This picture is from last year.
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A more current picture, different angle. It's in the center behind the pink Austin roses.

Any one one want seeds just email me.
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2 more I forgot
egyptian onion and
curly rush

Here is a link that might be useful: curly rush

hers's one---

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I have killed a Harry Lauder's Walking Stick! I love weird plants. I have something called a Caterpillar Plant, don't know if it will grow in your zone. Dranunculus is another strange and stinky plant. Sea Holly is cool, and I like rattlesnake grass and bunnytail grass too. Pregnant Onion is another oddity.

What about helenium "Autumn Lollipops"? They are cute and hardy. They have petals that are so tiny that you really can't see them unless you examine the flower up close!