Here's what you can get via oral sex without a condom:
1.Chlamydia - ridiculously common. it can live in her throat
2.Gonorrhea - also quite common. same as above
I wouldn't be worried about these. You can get tested and if you do have either they are easily cured with cheap antibiotics.
3.Herpes
This is incurable, and you can get HSV1 or HSV2 via this route.
4.Warts
If you don't already have HPV, you are in the minority. She'd have the warts on the area around her lips to have to transmit though. They don't have to be visible on her. This is also incurable.
5.HIV - extremely unlikely
6.Syphilis - extremely unlikely, and is curable too in case you ever do get it
THose are the most common STDs.
For random hook ups , always use a condom!!!! If she doesn't mind going without a rubber, stop and don't touch her. I once screwed a girl who tried to insert me without protection....i was worried for months. I got tested and was clean, but its not worth the worry.
Also, never go anal with random girls. You're just asking for it if you do.