The only solution to the leak is to replace the pinion seal. When the pinion bearing starts getting play in it it will bang and wear at the seal until it starts leaking. A loose pinion bearing will cause a vibration as well. This may not be your vibration problem, but while you are having that seal replaced it would be a good idea to have that bearing inspected at the same time.
Sure it'll suck, but it'll make you a man