I don't think it's possible. It would also be very difficult to go to Norway and apply for the Austrian visa during your stay in the US (it would be difficult - time wise - if you were a resident and not being a resident makes things even more difficult). As others have already commented, the length of your trips is also a problem, slightly over the limit for short stays, and would need to be adjusted to be doable with short-stay visas.
Austria being your main destination and apparently an important one (as you would be studying for 60 days!), I think the most reasonable course of action is to get in touch with the Austrian consulate and apply there first. Depending on what they tell you, you have two options:
- Applying for a Schengen visa. It could even cover both trips if you make sure to stay less than 90 days in total and get a multiple or two-entry visa. But I am not sure they would be willing to issue such a visa (as opposed to a single entry visa covering only the Austrian part of the trip), especially if that's the first time you are applying for a Schengen visa.
- Applying for an Austrian national visa. This would solve the length of stay issue and leave you free to apply for a Schengen visa from Norway afterwards. But I don't know whether a suitable visa is available from Austria, how much it costs, what would be required to get it and whether they would issue it for a stay that's under the short-stay threshold (when considering only the stay in Austria…)
In either case, when you apply, you should attach a letter explaining your plans carefully and why you want them to issue a somewhat unusual visa. But be prepared to get only a regular Schengen visa for Austria and to have to forgo your trip to Norway. I am just bringing bad news but also realise that a refusal is a very real possibility, you need to make sure your application is very strong to get even that.