Time for a little preventative (hopefully) maintenance. Pull the drive shaft out completely. Put it on your work bench, check both u-joints for play. Chances are at least one will be shot, maybe both.
After you put it back together make sure it is in phase because an out of phase DS will cause all kinds of vibrations.
Before you bolt it up look for excessive play on both the flanges. It is possible the oil in your picture is just normal wear and tear for an almost 30 year old truck. If everything seems tight, clean up really good around the flanges put it back together. Then keep an eye on it for additional leaks. If it does drip some more you know you need a seal -or two. If not you are good to go.
Roll around under it every once in a while, it is good for you and it!