My moms fiancé passed away suddenly recently. His will was from many many years and does not name her at all. She is still living in his house. Can his children - one who is the executor of his will- kick her out of the hose she has lived in for 15 years? Also can they just come in and take whatever they want from the house?

She was not mentioned in his will, therefore she has no legal standing in what happens to the home or its contents. Would suggest she seek the help of a good attorney before too much time has passed to see if she is possibly entitled to anything.

She needs a good lawyer ASAP. What state are you in? Most haven't even recognized common law relationships in a long time. So, as twinkie pointed out since she wasn't mentioned in the will and they weren't married she dosen't have any legal standing. However, they would have to legally evict her which takes at least 30 - 60 days so they can't just kick her out this weekend.

Without legal help the most she MAY be entitled to is half or what she can prove WAS hers.
Like a joint bank account and she can prove that money was deposited in there for her or by her.

This is one of those reasons that marriage is more than "just a piece of paper". If the state she is in doesn't recognize common-law marriages, then yes, the kids can legally kick her out and take everything in the estate. She is entitled to keep things that are obviously hers, and anything that she has title to (cars, accounts that she is beneficiary to, etc.). But the estate will be divided as the will states. And, to be frank, he had 15 years to change the will if he really wanted to provide for her.

As you have noted now, that Marriage is important for many legal issues.
So if she does not live in a state that reconises common law marriage she will actually have no rights at all. If the state reconises common law marriage then she will have to file in probate to contest the will.
But it is very likely the will will stand and she will have to move out with only her personal items.