Is there a place to make reservation only on Austrian railway website?

Not on the website. You can get reservations through their call center at 011-43-5-1717. Hours are 10 p.m. to 1 p.m, your time. The other option would be thru Raileurope, but they are likely to be more expensive. Check raileurope's prices first so you can compare when you call. You'll have the choice of 6-person and 4-person couchettes, or more comfortable beds in compartments for 3, 2, or 1 passenger(s).

Thanks for the info.

I also tried to make reservation through the trenitalia; it allows me to purchase, but it doesn't have the option of printing the ticket via email, and it says the option of "picking up the ticket at the self-service station" is n/a.

Should I call them directly?

Thanks!

No, you can't make a reservation only thru the Trenitalia site....besides, you won't be at an Italian "self service station," and, in any event, your American credit card won't work.
Call Austrian rail direct.