In this case using while and when change the meaning of the sentence completely. "I'll finish my homework when you help me with the dishes." So this is saying when you help me with the dishes, when the dishes are done, I'll finish my homework. The second sentence "I'll finish my homework while you help me with the dishes." This means that while you are receiving help with the dishes you are at the same time doing your homework. When you use while most of the time it means something is happening simultaneously. Ex: Mom was cooking dinner while chatting on the phone with grandma. Hope this helps!

They have slightly different meanings but both are correct grammatically speaking. while means you will do it together, at the same time. One person (you) will do homework and the other person will be doing the dishes to help you finish both at the same time. When tells someone that you won't do homework until they help with the dishes. You are waiting to start homework because you want someone else to help with the dishes. It would be the same as, "I will do my homework once you start doing the dishes." Let me know if you have any other questions. Good luck! :)