I live in Hackney Wick (five minute walk from the stadium) and there's not much around. There are a few trendy bars nearby on the canal (Crate and Bar 90) but they've been taken over by Hammers fans. Though, Crate has now banned anyone from wearing colours because p*ssed up Hammers kept jumping in the canal and being a general nuisance.
Westfield Stratford is next door, too, and there are some bars there. They will be packed, I imagine.
You could try Stratford itself, but I'm not versed on if there is anywhere to drink.
There are plenty of places to drink in Leyton (only a tube stop away).