Cleaning antique furniture

A couple of weeks ago, I held a garage sale. One item I decided to part with was an acoustic guitar which I haven't played since high school. A friend of mine came by and offered to trade this cedar trunk for my old guitar.

What a good deal! I traded a closet space hog in exchange for more storage space! I've decided to use it to house our Legos.

What I am wondering now, is what is the best way to clean it?

I should know the answer to this already, seeing as how I literally grew up in a wood shop. But most of my experience deals with building with wood, not preserving antiques.

I love all of the wear and tear on this piece. I know it is old, because of the manufacturer's tag in the lid, but I have no idea how to tell how old. Another thing I like about this, is that the legs match an antique dresser I have. The down side, is that instead of smelling like cedar, it smells like mothballs!

I initially cleaned the lid with a little water and Murphy's Oil Soap. It did a decent job, but it seems to have spots where grease has collected on it. Much like the hood over your stove collects grease, and balls up sometimes when you clean it.

I worked on the front of it for a while, where there seems to be plenty of grease effect. Perhaps it isn't grease, that's just how it behaves. This picture isn't the greatest, but you can sort of see the difference between the right and left halves, the right being the clean side and whitish haze left of center being the "grease" effect.

Anyone have any suggestions to bring this to life? I don't want to sand it and make it look brand new...I like the personality in it. But I'd like to properly clean it. What would bring out the natural color best? Tongue oil? And what about getting rid of that mothball smell?

Thanks,
Until next time,
The Good Monster