One labeled for wood or wood and metal. They usually look something like this:

I might suggest doing a bit more investigating before cutting the door. Frankly an oscillating tool isn't the best tool for the job but in any case you might be able to fix the problem without cutting the door at all. The odds are pretty good the door isn't hanging properly in the opening and could be fixed by shimming a hinge (or maybe two). Could you close the door and take a few pictures of the gap between the door and the jamb?

Second Mike's advice to search further before cutting.

Doors stick because the jambs have moved due to (usually) normal settling of the structure. The door slab does not move while the surrounding jamb sags on one side or the other or both sides. That pulls the door jamb out of square and causes the problem.

By removing material from the door slab, you actually allow for more movement and soon have an unsquare jamb and an unsquare door slab. Which means the entire assembly has to be replaced.

It is actually a much better(and long term) fix to resquare the jamb. That is not a difficult job, but not really a DIY job either, since a couple of tools are required. A level(I use a six foor long level for doors), a reciprocating saw(generically a sawsall), and several sizes of flats(to remove the door trim with out breaking/marring it).

There are, however, several You Tube videos illustrating how to resquare a door so a DIYer can get it done.

I'd take Mike's approach to look at the hinges first. Sometimes you can swap the bottom and top hinges and get them back into alignment. Or you can "swage" them with a hammer or vice.

Failing that, my tool of choice would be a hand plane. I think it would be tough to get an OMT to trim off a little bit of a door edge in anything resembling a straight line.

Oscillating tools are great...but I agree with everyone else that it's the wrong tool for this job. A sharp block plane on the top edge of the door is what I use. But it has to be truly sharp since you will likely be cutting across the grain in that location. Two other tips: 1) apply tape to both faces of the door as it will help reduce chip-out of the face grain; 2) only plane from the edge of the door inwards...if you do the reverse, you will break out chunks of wood on the door edge.

An alternative tool is a power sander to take the top edge down a bit. However, you need to keep it level to avoid rounding the top of the door over.

If the strike edge at the top is rubbing the jamb, I would first try substituting a 2 1/2" screw for the middle screw of the top hinge; sometimes (often, actually) the weight of the door is enough to warp the hinge area and make the door rub the frame. If the longer screw draws it tighter you won't have to get out a paint brush or anything.