From what I gather, you are not this man's wife so you are not these adult children's stepmother. They live like slobs and completely disregard your request that they pick up after themselves, and they aren't going to change. Their father MUST speak to them and say that they either shape up or ship out. Tell the father he must do this OR you will be shipping out (and really plan to do so).

What I can't figure out from your post is whether the boys ship in for household expenses. Do you work full time or part-time. Who pays the bills, etc. If you all work, perhaps the 4 of you can pitch in for a housekeeper a few times a week. If you work-part time and don't pay any of the bills, etc., maybe just consider it a part-time job or whatever, but I wouldn't knock myself out.

Have a "family meeting" and you make a list of things that you expect from everyone if you are stuck picking up after everybody all the time and doing the washing, cleaning, and cooking.

What it boils down to is your boyfriend has to talk to them. Like Dr. Laura would say, if the boyfriend doesn't respect you and marry you, why should you expect his kids to respect you?

I know it's a little harsh and I'm not one to give advice, but don't be a
"doormat" like I can be sometimes.