My washing machine (and whole laundry room) smells like dirty stagnant water. I've tried vinegar and bleach, nothing seems to work!

It could not just be your washing machine. Could be other things. Maybe your machine is not fully draining, maybe water from another drain gets mixed in with the water from your machine (it can happen), maybe there is something in the filter.

Your question was asked in another forum, I will post it and you can read through it:
smelly washing machine - MoneySavingExpert.com Forums

If nothing seems to work, you may need a plumber to come and look. Good luck to you.