I used olive oil to finish my salad serving utensils - now what?
Do nothing, or maybe give them a soap wash. 

You seem to be very worried about what are very small effects. Sure, the oil can oxidize over time. It won't turn your utensils into a big ball of funk. You probably won't notice that much difference in reality. Maybe, if you hold them under your nose, the whiff will be different than if you hadn't used olive oil. You can wash if you want to reduce the effect, or keep it so you can at least enjoy the esthetic difference of having oiled wood. 

Also, wood is not all that easily damaged, especially the kinds of wood a small artisan maker would use. People used to eat out of unfinished wooden bowls every day. Sure, you shouldn't leave the wood soaking in water, but you can wash it with detergent and soap now and then without getting much change in quality. I have a cheap, large-pore bamboo pan spatula which I regularly wash, sometimes with soaking, which is a worst-case scenario, considering the large pores of bamboo. It doesn't look 100% "like new", but it is still a normal, serviceable, nice enough spatula in appearance. The corners of the turning edge are slightly rounded, and the turning edge itself is a tiny bit frazzled, which could be repaired with a bit of sandpaper - but remember, this is something that gets washed regularly. 

If you are still very serious about getting that oil off, sandpaper is probably the way to go. But depending on the kind of surface the maker intended, you may ruin that surface. If you have small-detail carving, that would look much worse, since you'd have to remove a small layer of material, not just surface-polish it, and you may not be able to get into each carved hole/chip anyway. And if the set was not intended to look too rustic, you will need to go through a progression of sandpapers applied with some skill to get a nice, even sheen. 

Also, remember that those are salad utensils. If you intend to use them, as opposed to hanging them on the wall, they will come into contact with edible oils frequently, as well as ingredients like vinegar and lemon juice. Especially if you wash them rarely, and/or use little soap, they will get a "seasoning" of salad dressing on their surface just from use. Yes, it will get slightly rancid, and all that. You will likely get a visual difference between the heads of the utensils, and the dry-staying handles. That is normal and expected with wood utensils in use. If you want to keep them pristine, the only chance is to get some heavy acrylic or nitro finishing on them and keep them away from food, in a room different from the kitchen.