jcowdin is on it. Sounds like the seal on the passenger side diff housing has worn and is allowing gear oil to pass by it, if I am understanding your description correctly.
The housing seals on the passenger side of these trucks do wear down over time and leak. With the stock fixed hub locks, the front axles continually turn, even if you don't have 4WD engaged. There is no carrier bearing on the passenger side, only the oil seal. The CV stub simply pops into the side of the diff into the side gear of the differential... which allows some up and down movement of the CV shaft shoulder when driving - which when combined with the constantly turning CV axles, causes more wear on the lower seal surface until it erodes away. Suzuki now sells a bushing that is supposed to reduce this wear. I have never tried one. maybe someone else has and will pipe in. Installing manual hubs reduces the wear on this seal too, because when they are unlocked, your wheel turns but the CVs don't.
The replacement seals aren't that expensive nor difficult to remove. In fact, you can remove the old seal and knock a new seal back in with a large socket or seal installer in probably less than 5 minutes.
However, the devil is in the details. Drain the gear oil. To access the seal area you either; jack the front of the truck up, support the truck with jack stands safely on the cross member or frame rails, then remove the passenger front wheel, disconnect the caliper and hang it by wire out of the way, disconnect the sway bar, tie rod and remove the strut bolts to allow the control arm to be able to drop (with a jack under it to control its movement slowly) then pull the snap ring and washer off the outside of the CV axle which will allow it slide out of the hub, then remove the CV stub from the housing by carefully prying/tapping/rotating the CV so it pops out so you can access the housing to get at the seal. Don't tug on the outside end of your CV. Sometimes they can put up a fight and you have to go at the tapping with a BFH. There is a small "c" clip on the stub end of the CV shaft inside the diff which can hang up on the lip, hence rotating it when your are prying sometimes helps it release easier. Make sure the little C-clip is still on your stub end when it comes out. You don't want it floating around inside your diff. It is hardened steel. If it isn't there, chances are it popped off inside your diff and you will need to split the diff and go after it.
Alternately, you could remove the 4 bolts to the front drive shaft, tie the drive shaft up SECURELY, remove the 2 bolts securing the nose of the diff to the cross member, then remove the 4 and 3 mounting bolts from the housing on each end OR remove the 2 bolts holding the housing brackets and attempt to wrestle it out that way. My experience is you also have to remove the front bolt from the front passenger side control arm and ratchet it downward about an inch to allow clearance for the CV to drop enough to pull/come out. It also helps to remove the four bolts holding the rack and pinion and push the R&P upward for needed clearance. This process works (IMHO) better if your truck is on a lift versus jack stands.
Personally, I would NOT attempt the alternate method by myself. Two sets of hands are "more better" and you will probably still fight the CV to get the housing to pull away from the CV. The front housing isn't super heavy but it sure is awkward. Especially when you are trying to extract the CV stub at the same time.
Assembly is reverse of the above. Make sure to coat the end of your CV stub with a coat of grease so it slides easily into and by your new seal.
