Yes, it looks like every train will be affected because the line out of Marylebone is totally closed on that day for works.

The crucial phrase on the National Rail site is this one:
"Trains to/from Birmingham will start from / terminate at Oxford or Bicester North. [...]"

i.e. south of King's Sutton station, some Chiltern trains will be diverted on a different line to Oxford instead of using the normal line, whilst other Chiltern trains will use the normal line for a short distance but then terminate at Bicester North (there'll be no trains running south of Bicester North station).

You've basically understood it right - travel from Paddington to Oxford on a First Great Western train (of which there are many), then change there for a (diverted) Chiltern train to Stratford (which will start from Oxford). It's possible that the Chiltern trains from Oxford won't be going to Stratford (they might be the ones starting from Bicester North) but will be heading to Birmingham instead, in which case you'd need to change again at Banbury for a Stratford bound train - in the absence of a timetable being made available, one cannot tell, but it should be available sooner or later.

The engineering works map (PDF) on the National Rail site is useful - you might like to compare it to Chiltern's regular route map (PDF), where you can see that in normal conditions they run a handful of services to/from Oxford (only late at night I think).

These changes aren't yet appearing in the journey planners presumably because the temporary timetable hasn't yet been finalised - there's a lot of upgrade work happening on the Chiltern route at the moment which is running behind schedule, which might help to explain matters, but it certainly seems pretty slack that they don't appear to have worked out exactly what they're going to do in terms of what trains they're going to run yet.

And as a wider comment, yes, engineering works information often leaves something to be desired - pieceing together exactly what the plans are can sometimes feel like you're a latter day Sherlock Holmes searching for clues - one thing that should be remembered however is that trains can be diverted to run on all sorts of unusual routes, which can serve to confuse if you're not aware that certain connections exist.