As Emery said, check the tires for damage, proper pressure (try inflating to max press. stated on tire), also check the lugs and also check for mud inside one or more of the wheels. If it doesnt begin shaking until highway speed, its not the engine, and its very unlikely its the transmission. Most likely wheels/tires, secondly something with driveshaft/flex couplings.

Whine is unrelated as you noted it steering, check belt and fluid. Oil pressure possibly too low viscosity, check against owners manual recommendation. Oil consumption, start with leaks, then diagnose from there. Valve guide seals are a distinct possibility if no external leaks are found. Good way to check guide seals, find a long grade, or take foot off gas and let it slow down to a stop from high speed. If you then step on the gas and see smoke out the back, its likely guide seals.