My best sources put it at 120m long, which is Technically Size 4. However, the ship is small and uses space inefficiently, so let's call it Size 3.
Size 4 covers 800-1300 SU, Size 3 covers 600-1000. I'd guess off hand that an Oberth runs 600-800 somewhere. Call it 700.
An Oberth Class Escort, Courier, or Transport would have a crew of 21. An Oberth Class Scout would have a crew of 42. As a Research/Labratory ship, it would have a crew of 56.
The TNG Rulebook says the Oberth has a crew of 80, but then it also says it's 160m long and calls it a Surveyor.
If it were a 1300 SU Scout, the crew numbers match perfectly. A 1000 SU Labratory Ship matches even better.
Now, let's get silly.
As a Frigate, it would have a crew of 161. As a Cruiser, 175. As a Surveyor, 210. As an Explorer, 252. Lastly, as a Medical Ship, it would have a crew of 294. Mighty crowded in there..