You're correct in that you can't use a 16-25 railcard with a season ticket. This is going to be very expensive, and if you can't afford it it might be worth exploring alternatives. However, there are a few things to think about, rail-wise.
First of all, you'll want to know whether or not you need onward travel in London. Trains now travel between Oxford and London on two routes - the Great Western which arrives into London Paddington, and the slightly-but-not-significantly-slower (and arguably more comfortable) new Chiltern route which arrives into London Marylebone. As far as I can make out, there are (oddly enough) no fares valid on one route but not the other, meaning there is effectively no price difference between the two routes. But if your destination in London is nowhere near either Marylebone or Paddington such that you would likely be taking the tube every day, you might also want to get a ticket integrated with a London Travelcard, which will add even more to the price.
Without a London Travelcard (that is, valid only to Marylebone or Paddington), a season for 2 months and 20 days will cost you £1259.60 (use the season ticket calculator on that page). This seems to me, ignoring the possibility of any fare loopholes (I don't know of any of particular note along that route), to be the cheapest possible option if you're travelling in the peak.
Ask your employer (I'm assuming you have an internship?) if they'll do a season ticket loan scheme, if you think you can afford this but don't have the capital to buy it all at once. It's cheaper than buying weekly season tickets (at £126 each - @Calchas's figure of £123 is not correct, as those fares only work for seasons a month or greater in duration).
Using a 16-25 railcard with Anytime Day Returns, assuming you're travelling every weekday, comes to about £2400, obviously significantly more. Using off-peak day returns with a 16-25 railcard, the price comes to about £1000, which is cheaper, but would restrict you to travelling on trains arriving in London 10:00 or later, and would prevent you from using some of the faster trains from Paddington in the evening peak (there are no such evening peak restrictions on the Marylebone route). I'm guessing since you said you'd be travelling in the peak that this would be no good for you. If so, the season will be your best bet.
If you need onward travel in London, it gets even more pricey. A weekly travelcard season is £147.70. A travelcard for 2 months and 20 days is £1465.40. An anytime day travelcard is £45.50, and an off-peak day travelcard is £19.80. If you need onward travel in London but don't think you'd be doing much travelling there besides for your work, it might be worth checking if Oyster or Contactless would be cheaper for you. See the single fare finder (remember you can load a railcard onto an Oyster Card), and the Oyster caps for railcard holders and non-railcard holders.
I hope all this helps.