The best advice I can give you is to sister some new temporary joists to the existing. They'll either be 2x10 or 2x12 that you'll need. Do not remove anything existing either,as you could easily compromise the structural integrity that's there now.You'll have to pull down most of the drywall on the ceiling to accommodate the sistered joists,as you'll have to join the temporary joists as far back onto the existing where there is no water damage with an overlap of at least 6 to 8 feet on both ends,or worse case scenario, all the way to your top plates on the outer walls. If the joists are bad enough, you may need to sister on both sides of the existing with cripples in between the joists for more structural integrity until you can properly fix the problem