If it drives well and got you home, and has no engine light on, I reckon you're OK. Engine smelling of hot oil sounds like cam cover gasket gone. With engine hot open the bonnet and see if you can see smoke rising either side. If you can, that is the side that has gone. Changing it is quite a job, involving taking off the entire inlet manifold. It will have been caused by blocked breathers, so that will need doing as well.
When I buy a used Omega I always make sure I can undo all the wheel nuts, then jack it up and see if I can get the wheels off. If you have a decent jack and an axle stand, you can support it safely to allow you to inspect the steering, suspension, exhaust, etc. If you cannot get nuts or wheels off come back here, get advice, and get them off.
Check that all the lights work, and all the electrics, wipers, horns, washers, radio, etc. they probably do and that will comfort you. Change air filter and pollen filter, they are easy, fuel filter is trickier, do it later.
Good luck and welcome to the forum. You will get lots of good advice here.