There are many good products that you can use. My recommendation is find one that says it is boiled linseed oil with a drying agent added. Boiled linseed oil is what is put on the finest gunstocks. It will give you a good depth of finish and bring out any grain that may be present.
Be sure it has a dryer in it or it can take FOREVER to dry.
One nice thing about linseed oil is that if you ding the handle up a bit, you can touch it up with a little sanding and some more linseed oil.
Put on a minimum of five or six coats, rubbing down each coat after it is good and dry with 0000 steel wool.
Some people don't rub down the last coat. I like a satin sheen, not a high sheen, because I think it looks a little "classier", so I rub down the last coat with rotten stone (a very fine powdered pumice). You can get it a good paint stores.
Tung oil is easy to put on, drys fairly quickly, and looks very nice. But, in my opinion it darkens with age. (not necessarily bad -- but know what you are getting into).
With the linseed oil, take your time, rub just a SMALL amount in by hand, rub it a lot. You are literally rubbing it into the wood. Add more as needed.
If your knife has a finish on the handle, and I assume that it does, you might want to sand it lightly with some 400 grit sandpaper (or higher) to knock off the top of the finish so that it will take the new finish into the wood. If the finish is heavy you might need to strip it off, but the way you describe the knife as "dry" It sounds like it has very little finish.
Good luck,