Stats have no impact on the egg buff, so get a low level one to safe time and eggs. The egg buff will only occure when the Oviraptor is set to wander, just fill it's inventory with junk to make it stationary. The buff does additionally not stack, so getting more than one only makes sense if you need to cover a bigger area.
The Oviraptor will eat meat once tamed and does not increase the chances for mutations or multiple hatchlings.
Everyone needs to know and it is dev confirmed that Oviraptors DO NOT buff chances of mutations or twins or triplets. This is a long going myth that needs to be shut down. Any twins or triplets you are getting is purely coincidence. This was said by one of the devs on twitter!
These guys can steal eggs without aggroing surrounding dinos! You can get easy wyvern and rock drake eggs! Put it in a cryo pod, sneak into a nest, pop it out of the pod and have it set to follow close, run to the other side of the nest and when it gets to the nest it will take the egg. Once it has the egg you can take the egg from it and there won't be any aggro. Just make sure you don't switch the egg out of your inventory because you'll get the aggro then. Rinse and repeat for super easy wyvern and rock drake eggs!