Pic of worms...I know its hard to see, but some are about an inch and vary from whitish to green and some are only about 1/2 an inch and have some little black spots on their backs.

Any squash growing out of a compost pile is likely to be a hybrid of several squash grown during past years.

Acorn Squash but not sure I would eat it if it is infested by worms unless there is enough of the meat to be worth while as we bake them.

Jean, thanks. That's a possibility, but this is our first year garden and most of the scrap additions from friends and family would be organic store bought or farmers market purchases.

Wally - this one seems ok. Never seen an acorn like this! (so maybe it is a hybrid) I submerged it in a bucket of water and about ten worms came out! The three other squash were toast along with two huge butternuts and some cukes. Insert cuss word here>>.

Any advice on dealing with the worms?

Not really, They look like pickle worms which are difficult for a home gardener to control. They really mess up cucumbers, squash, and muskmelons.Here I can get ahead of them early, they arrive around the Fourth of July and late they leave for Florida around Labor Day. Overwinter in Texas and Florida.
Squash are quite promiscuous so any volunteer is usually a mixed breed. Winter squash are resistant after the rind hardens, but young tender ones are fair game.

Looks like it was Acorn squash. I'm sure it had better days though.