woods that match teak?  

....
I'm on board with creatively "accessorizing the beast", as suggested above-

I am absolutely trying to...
I am absolutely trying to polish a turd with this piece. I figure there's no way I can make it worse though. The reason I'm even getting this piece is because I have to buy it with a dining table and chairs that are too good to pass up.

I say...
keep the top tier and somehow gracefully mount it to the wall, re-inventing the piece. The bottom section should be put to sleep.
Aunt Mark
edited to correct poor speling.

I'd do black legs.
I like teak and black together. I remember seeing a lot of it in the Illums Bolighus department store in Copenhagen in the 90s, when I was just becoming aware of real Danish furniture (vs. the Sears "Danish Modern" stuff of my childhood).

just wondering, does the...
just wondering, does the lower portion of that credenza have a solid bottom to attach the new legs to?
I have had a couple of less expensive teak wall units similar to yours and the lower bottom front portion was just an apron instead of a solid bottom (kind of like a toe-kick in a kitchen cabinet if that makes sense)
If you do have an apron style front on the bottom you might end up needing to add some blocking to have something to screw the legs into.
ok back to lurk mode for me. good luck with it!
cheers
brian

It is likely
that the plinth/ skirt is structural support and is the support equivalent of the long support boards under a credenza with legs. If you dont remake the undersides along those lines you likely can look forward to major sagging with door binding and other problems. On an aesthetic note, these plinth based pieces are generally equated with later (read cheaper and poorer designed) pieces. You might take a look at some of Wegner's and Robsjohn - Gibbings cabinets of similar designif you do not know them already. It helped soften my dislike of plinth based cabinetry. If it were mine I would either learn to like it as is (though I would remove the top) or pass it on and hunt down a legged one. I think it would be more trouble than it is worth to properly support the case, and it is likely the proportions/ look would be off enough to not be very satisfying. Then again it is just piece of furniture, so have at it.

I have to agree --
completely. The structural issues are well-pointed out -- and for my money the piece will look top-heavy with that full-width "hutch" on top and inboard legs at the floor. But who knows . . .
I'd learn to love it (it's really far from ugly, as I see it) and move on to something else.

...and here is the entire...
...and here is the entire pick...

Maybe a good idea in theory.
And one that's crossed my mind, too... for the few seconds it took to realize that it would be more trouble than it's worth as glassartist said above.
Post the shite on craigslist with "Danish/mid-century/teak" in the heading for $100 OBO and put any proceeds toward quality items. You'll be happier.