Try squirking sections with Fantastik and covering with warm damp rags for about 10-15 minutes. I did this to remove an old linoleum floor, put down directly over oak. The waiting is important--and I then used a paint scraper/compound knife to scrape up old paper backing and glue. Mopped up a lot of the old glue with the wet rags, then let floor guys get the rest with the sanding.
Messy, but it works

Thanks! I'll try that tonight. Mine's oak too. Why on earth anyone would cover an oak hardwood floor with linoleum is beyond me, but anyway......

You might want to try a heat gun on low setting or even a hairdryer to loosen that glue.
The previous owner used an unknown type of glue on a floor in one of the rooms in this house to keep and area rug in place....Chemicals didn't touch the glue but heat softened it up enough I could get most of it off. I can still see where the glue was...hopefully when the floors get redone..sometime down the road I won't see it.

If you have it resurfaced, you should not see the glue. The resurfacing basically removes the top layer of wood, so there is a limited number of times you can do this to a floor, and then the surface is sanded and treated with urethane.

We had a very badly gouged floor, and had this done, and the result is great. It would probably remove the glue residue pretty well.

They may have put down linoleum if part of the hardwood was too damaged to repair (such as water damage rotting the wood), and did not want the expense of putting in a new hardwood floor.

I successfully removed an entire room of linoleum paper/glue from a 1910 home by literally soaking the floor with a warm sudsy water. I then used a scraper (the straight edge of a flat shovel, actually) and painstakingly scraped away. The soaking helped to loosen the paper quite nicely. The water was absorbed by the paper and was easily removed with scraping. I then lightly sanded the oak floor which removed the remainder of any stubborn glue. The floors look great, and the water did not hurt them at all.

I removed the underlayment with just warm water. Not even any soap (though it couldn't hurt).

Really old lino was glued down w/ 'hoof glue', which is water soluable.

We used very hot water and an old fashioned string mop and rolling bucket that has the squeezing out thing for the mop. Like a janitor, we sloshed the hot water on, waited until the (hoof) glue turned grey and soaked it up, sloshed it off. Took 2 or 3 fresh buckets over the whole floor to get it off, but after it dried the floor was sanded and came out fresh with the beautiful old grain.

Thanks for everyone's suggestions. We tried warm water on one spot and it didn't make things much easier, but I assume that was because I was afraid to leave it on very long and damage the floors. I think I'll have to take that chance and let it really soak in to see the results you guys had. I know what I'll be doing all weekend.

I used Goof-Off. I also had a 1905 house with linoleum stuck to the floor.

peel-
No one else has brought this up, so I'm afraid I'll have to. That vintage linoleum flooring is about 99% sure to contain asbestos and so might the adhesive. Whatever you do, you do not want to be sanding and scraping this stuff, and contaminating your family and household. It will release particles that are a serious health hazard. I'm not going to give you a big lecture here, but you might want to do a Google search on "asbestos +flooring" before you proceed further.

Unless the wood floor is a premium grade product tearing it out and replacing is liable to be faster and cheaper.

GaleForce-
There are a lot of things to be aware of with such a removal. Here is a link that discusses this problem in pretty clear language and lays out the options:

Flooring removal

Thanks kudzu. Interesting link.

Well I feel like a jerk for not considering asbestos before, and we have already removed 95% of the paper backing using a razor blade scraper. But because of the concerns you guys raised I am sending out a piece to be tested before we do any kind of sanding, and I am going to be covering the floor with something until we get the results back so we don't kick anything else up. What's done is done, but hopefully we'll be able to proceed as planned once the results come back. If it does contain high amounts we'll get someone in to test the air quality before we make any more decisions.

peel-
Sorry to have raised this, but better you should know. If it's any comfort, I did something similar a number of years ago...and I should have known better as I worked in the environmental field. What's done is done and the good news is that you won't repeat this in the future. While I have a very healthy respect for asbestos, it's also important not to obsess about this. Anyone who has remodeled a house has probably created such hazards due to the prior use of asbestos in many products (flooring, adhesive, joint compound, ceiling tiles, furnace insulation, mortar for firebrick, etc.) If such exposures were uniformly dangerous, most of us would be dead. However, I like the odds in my favor: keeping future exposure to a minimum makes a lot of sense.

Thanks, kudzu9. I'm not all that concerned about it....I know most people who have developed problems have been in an occupational field where they were constantly being exposed to materials containing asbestos. I'm just glad I didn't start sanding....don't want that stuff recirculating through the ductwork!
I haven't gotten the results yet...maybe tomorrow.

I'll just add my two cents (before I go back to peeling, scraping, removing).

Using water (or any other liquid) greatly decreases the friability of any asbestos that may or may not be in that old lino underlayment.

Sanding anything in an old house seems...risky.

If you sand the paint, you can release lead, if you sand off the underlayment, you can release asbestos.

We're a 'strip' or soak house. We don't have kids, but we have lots of friend's kids in the house, and we don't want to take any risks with them, or ourselves.

The joke is that we're not that bright to begin with, so we can't afford to lose any brain cells.

Well I got the test results on Friday....we are asbestos free!
Thanks to everyone for your advice!

Woo hoo!!!!!!!!