The transfer case is a Borg Warner 13-54. The T-cases on these models are very strong and last for a long time. Bearing problems at 150k miles would be unlikely, unless there was a defect or the unit had problems internally, or fluid maintenance was not done.
Both t-case output yokes are splined if I recall correctly. Check that the retaining nut is tight on each. This will require a 30mm thin-wall socket. I bought a 30mm impact socket and had a machine shop lathe it down to fit.
The T-case is real easy to tear apart if you want to check out the inside.
It is pretty easy to remove the transfer case. I have done it several times by myself and it is about a 30 minute job once you get good at it. Drain the fluid by removing the vibration damper and then drain plug. Remove the skid plate, four bolts. Undo the driveshafts at the t-case yokes. You can just let them dangle. Remove the electrical connectors if you have an electronic shift t-case, and the t-case speed sensor. Remove the vehicle speed sensor. Disconnect the breather tube, which is just rubber tubing. Five bolts hold the t-case to the transmission. Three are accessible from underneath easily. The top two can be removed from underneath (very hard) but it is far easier to pull back the carpet, remove the transmission access panel in the floor, and remove the bolts through there. Not necessary to remove seats or console to get at the panel. Pull the transfer case backwards off the locating dowels and trans output shaft (splined) and lower it down. I believe the weight is about 72lbs so you can remove it by hand yourself if you have a little bit of muscle. I am a skinny 25 year old and can lift the t-case in and out by myself. Using a jack is just awkward and you risk dropping the case. If the factory gasket is present between t-case and transmission, try to preserve it, but RTV will work if the stock gasket is destroyed. I could not easily find a replacement gasket.
Once you remove the t-case, fluid will dribble out the back of the transmission if you have an automatic. There is a small hole that it dribbles out of in the extension housing. I jammed a coarse thread self tapping screw into the hole to plug it temporarily. The aluminum is soft enough to accept the screw and you won't hurt anything. Just remember to remove it before re-assembly.
Once the case is out you can split it; remove the yokes (30mm thinwall socket) and shift motor (e-shift) with t-case speed sensor if you haven't already done so. 9 bolts hold the front and rear halves together. Use a prybar (Ford says so!) on the bosses provided to split the case. Inside is the guts of your case and it's really not too hard to tear apart and re-assemble. Before re-assembly, clean the case halves and apply new RTV to the mating surfaces.
Common failure and wear items are the low range shift fork wear pads. These plastic pads wear out over time and can allow the low range gear to walk balk and forth and try to engage at cruising speeds. The pads themselves, when completely worn out, often disintegrate and plug the t-case oil pump's screen. Stock wear pads are white opaque plastic so they're easy to find. Replacement pads are available with some searching. They were used on several t-cases and some transmissions.
While you're in there, replacing output yoke bearings and seals are relatively easy. The seals are not too hard to find and I know RockAuto sells a complete new bearing kit.
If you start on this process and want more info on it, or scans from the Ford Service Manual which will make it easier, let me know.