I live on this line. We've got off lightly as they were going to shut for two weeks solid.
Anyway, in the past Stratford has been served by a shuttle from Leamington Spa, so you'll be looking at three trains minimum. This should however give you the option of taking Cross Country from Reading or Oxford to Leamington.
Is it worth seeing if you can go via Birmingham (so Virgin up there, then whoever operates straight down to Stratford)?
The replacement timetable should go up very soon - click through from here
http://www.chilternrailways.co.uk/ti...-times/changes