Should I move onto Daggerfall, Morrowind or Oblivion (my brithday was Thursday March 24th and I got Morrowind GOTY and Oblivion GOTY both for the pc)

Play DF for 6 or 10 years :>

Play in chronological order

If you have the chance to play them in order, I highly recommend you do!

Don't forget Battlespire and Redguard (if you can find a reasonably-priced copy of those) in between Daggerfall and Morrowind. They're fairly fun games themselves, actually

I would recommend playing them in order. I am finishing up Oblivion again, after having replayed the previous 3 games.
As Maccabeus stated above, Battlespire and Redguard are both enjoyable games also

Play them in order!

After having played Morrowind and Oblivion I found it very difficult trying to get into Arena and Daggerfall. It's just that everything in the games is so much different that it just doesn't translate well going backwards.