Well, from what I can see, and from a carpentry perspective, I think the easiest solution is for you to buy 1 x 6 red oak boards from Lowes, put a light coat of wood conditioner on them before you stain it in red oak, spray the dried boards with two light coats of canned satin finish polyurithane, and then cut the butt ends at a 45 degree angle to fit into the 45% outward sides of the legs. Nail the top and bottom edges of the boards into the top and bottom ridges of your train sides using #6 finish nails, countersunk and filled. Be sure that the top edges of those boards are flush with the top of your train table.
The outside edges of the legs will still be a light color, but the whole thing will flow nicely. Do not try to stain the legs with a Red Oak colored stain. The white wood will not take the stain well and it will look blotchy.
You can then buy thin, flat, wide pieces of red oak at Lowes, that are about the thickness of a yard stick. I think you can get them in up to 4 ft. strips. Finish those just like the side boards, and gently nail them on top to cover the gap between the top of the table and the side boards, using #3 finish nails, countersunk and filled. I think that these strips are about 4 inches wide, but if you can't buy them wide enough to cover the gap, then you will need to buy more 1x4 boards, and cut them lengthwise (rip them) to the proper width. Not that hard to do if you have a table saw or you tack the boards down on long piece of 2x6 pine and then cut them into strips with a 7 1/2" circular saw, using a shallow blade depth. (Just go slow and be very careful you are not cutting very deep into the pine board underneath.)
Red Oak is not cheap, but as you can see from Mike CT's photo, it can be quite beautiful when properly finished, stained and sealed.
Hope this helps.
Mannyrock