I purchased a 1987 Sammy and the guy stated the the transfer case had a 2 High/Low and a 4 High/Low.  Can anyone explain this to me.  Also when driving it at 50mph I get a lot of hum from the transfer case stick.

Help a new owner out.

If it has still just got the single shifter, he probably just removed the center detent ball so you can use an alternate shift pattern to access 2wd low.  It works, but can be a PITA to get in and out of 2wd low at times.  Twinsticks are definitely a better way to access it.
If the samurai is lifted, the vibration is probably coming from the rear driveshaft.  If the ujoint angles do not match (or very very close), then you will get vibration and it can be transferred up through the driveline to the tcase.

What would be a good recommendation to correct the noise?  Also would putting twin sticks in be a better options.

What would be a good recommendation to correct the noise?  Also would putting twin sticks in be a better options.

Check the angles on the rear driveshaft ujoints, to see how close they are to the same angle.  Also check to make sure the ujoints aren't loose.
You can also check to make sure the transfer case mounts are not torn.  Lay under the samurai and push up on the tcase...if either side of the tcase lifts off the mounts, then you have a broken/torn rubber mount.
Personally, I like the twinsticks over the single stick with the alternate shift pattern.  I have ran both and prefer the twinsticks hands down.