score:5
Since you're leaving from Tartu and Riga is a viable alternative to the Tallinn airport and a much better option as a flight gateway.
According to the flight schedule Air Baltic has at least 6 scheduled daily flights to Oslo/Gardermoen including 1 at 22:00 and one at 23:05, which will suit your schedule nicely.
You're right about the buses from Tartu to Riga. LUX Express doesn't seem to have a very convenient schedule, neither does Ecoline.
As far as airports are concerned the only other airport within a reasonable vicinity would be Pskov but nothing worth mentioning is flying to or from there. The next major airport would be Pulkovo but personally I wouldn't bother with it.
ADDITIONAL INFO After checking flight schedule from Pulkovo to Oslo I really wouldn't bother...