Welcome to the family.
What you have bought is known as a part-time 4WD, and as you have learned, should not be used if 4WD on any "high traction" surface - when a four wheeled vehicle turns a corner, each of the four wheels turns at a different speed, the front turns faster than the back, and the outer turn faster than the inner - part time 4WDs don't have the center differential that's needed to allow this, so the wheels need to be able to slip to prevent what is known as "drive train wind up" - chances are you didn't damage anything - since you haven't reported any loud bangs or major oil leaks - the common damage areas are the transfer case and/or the front differential housings, and the damage is usually catastrophic and very noticeable.
Regarding the oily residue on the sump and differential - start by washing it off with your choice of degreaser and then watching it to see where the leak is from - I believe they use silicone rather than the old fashioned paper gaskets on both the sump and differential. Pay close attention to the oil on the side of the sump - it probably does not come from the sump - but is dripping down from a leak higher up - the cam position sensor (on the back of the left side or exhaust cam shaft) is fairly common, as is oil spilt and not wiped up whilst changing the filter.
One of the things I do will all "new to me" vehicles very shortly after purchase is a full service, making sure to replace all fluids & filters, the drive belts and spark plugs.
Sorry I can't be much help on the steering - that's one of the areas where your car differs from mine - I have rack & pinion, you have the older style steering box - whilst servicing check for play in the linkages and replace where necessary.