You can pick for immediate use as soon as the skin is hard enough that you can't puncture it with your fingernail. At this point, most varieties are white-ish with a hint of green or yellow. To store, they need to fully ripen on the vine, roughly 4 more weeks, in my experience, beyond the stage above, although longer is better on the vine if not in danger from pests, disease, or weather. By then, the basic S.S. is yellow-ish in color, as the yellow deepens as it ripens.

a little google research will certainly help. first it takes more than 100 days of growing. over 3 months. in new england that means the entire summer season. therefore harvested in the fall as late as one can usually. however Wikipedia has info. When kabocha is just harvested, it is still growing. Therefore, unlike other vegetables and fruits, freshness is not as important. It should be fully matured first, in order to become flavorful. First, kabocha is ripened in a warm place (77 °F/25 °C) for 13 days, during which some of the starch converts to sugar content. Then it is transferred to a cool place (50 °F/10 °C) and stored for about a month in order to increase its carbohydrate content. In this way the just-harvested, dry, bland-tasting kabocha is transformed into smooth, sweet kabocha. Fully ripened, succulent kabocha will have reddish-yellow flesh and a hard skin with a dry, corky stem. It reaches the peak of ripeness about 1.5–3 months after it is harvested. I live in new england zone 5 and would recommend that it grow as long as possible then finally harvested on the date before the first night freeze. at which time there should be some fully ripened colored squash and some obviously green squash. I would keep all of them indoors at room temp and the green ones should ripen over the winter. tasting better as time goes on but ready to eat when you want to serve them up. even a ripe when picked might not go bad until spring. but it is always best to eat the ripest ones first.

I can't speak for Spaghetti Squash, but Acorn squash is ripe when it is a very dark green (most varieties), gets an orange spot where it was touching the ground, and is hard to dent with a fingernail. Acorn squash ripens fairly quickly, relatively speaking, and is not as finicky about being 100% ripe to be tasty (but does not store as long).

No they can't get too big. Anytime frost threatens, time to harvest it all. When the vines are dead or almost dead, harvest (as in your last photo of delicata). When the thumbnail test says the rind is hard you can harvest. Your butternuts look a bit green still, and the plants still have lots of life, so if there is minimal threat of bug or critter damage, more time on the vine would be great. Acorn will have an orange blush on one section when it is ripe. I've read that lifting delicata up off the ground on, say, a plastic coffee can lid to prevent rotting while it ripens is a good idea. Your one scrawny delicata might just be insufficient pollination. I actually disagree with some of what is in that linked article: fine to leave curing squash out doors, just not on the ground (a deck or porch is fine.) Best storage conditions for squash is around 55 and DRY(colder, 40 as they say, not necessary and can actually detract from storage and flavor. This same organization has another article that states this. They are not editing very well.). Also, I would not recommend a garage or basement -- too humid, and that causes rot. A cool bedroom is great. Also, cut or bruised butternut need not be eaten asap -- it normally heals just fine and butternut will not taste it's best until at least 2 months storage. So put the damaged squash in a separate box and watch it closely. If there are any signs of rot, then go ahead and eat it. But I have had deer bitten butternut last until the next June, no problem.