question about the condition of a teak credenza  

hah
tktoo, I'd totally take up on that offer if we live nearby!
Speaking of cleaning, is there anything I can do to make the grain pop more on this piece? I have a suspicion that there is grime and residue from household cleaners on it. Some people swear by feed-n-wax. In the past, I have simply used teak oil to wipe off the surface but that was on pieces where the grain was already very vivid.

I'm 35 miles from Boston.
Standard cleaning involves a good rub-down with either mineral spirits or (I prefer) naptha on a clean rag (I like linen) applying appropriate amounts of elbow grease. Wear gloves, work in a well-ventilated environment, and follow fire safety instructions on can. Refold your rag often to expose clean surface and to avoid simply redistributing any grime. Neither of these will damage a finish (or bare wood, for that matter) and will remove 99% of grime and old wax.
After that, it's time to assess the composition and condition of the existing finish. Often, all that's necessary is a fresh coat of paste wax and buffing. Butcher's, Minwax, Briwax are all good.
I'm not sure exactly what you mean by making the grain "pop". From your photos, it already looks pretty "popped" to me. Really, the piece seems to be in very good condition, overall. I'd stay away from those hardware-store-variety miracle finish restorers in a bottle. You're asking for trouble there.

Sounds right.
to me. The finish looks pretty clean and clear in the photos -- the fact that the top is reflective means that the finish there is glossy and thus transparent (barring some odd clouding of the finish -- which doesn't seem to be the case).
The only way to further enhance (exaggerate) the figure would be to strip the finish and apply a stain which would adhere to the softer (darker) grain features, followed by sanding and refinish. And I don't advise that move at all. A cleaning and waxing should be pursued.
(I've found that a little powdered cleanser on a damp sponge is a quick way to remove stubborn grime, either on a small area or over the larger surface. This works well with matt-finished laminate, as well. However, too much rubbing will immediately start to remove some gloss from the finish (and will begin to glaze matt laminate) -- so the minimum of friction is recommended. The application should be followed by a clear-water rinse -- and in the case of wood, immediate and thorough drying. I mention this only as an alternate to the naptha wash, reserved for cases where that doesn't achieve all of the desired effect.)

any tips on a safe move?
We are picking up this credenza from the seller's house this weekend. My SO and a friend will be doing the heavy lifting.
I am planning on removing the drawers, tape the doors shut with paint tape, wrap the credenza with some moving blanket and tie the whole thing. Not sure if the blankets are necessary as there's nothing else going in the moving van and we are only going 5 blocks. Any thoughts on if this will work or whether there is a better way?
I am starting to get very excited!

I would
Lay it down on the blanket on its back side, and secure it with belts.

5 blocks ?
You could balance it on the roof !
No, really, the drawers are more safely transported in place in the cabinet than anywhere else. For a long trip, drawer cabinets shouldn't be moved on their backs if the drawer fronts bear on the face frame and support the weight of the drawers. Upright and blanketed is the best thing, in that case. For you, on its back on a blanket, no wrapping if nothing else is going to be transported. Don't overthink it. . .

and DON'T tape anything.
you risk leaving residue behind on such a high gloss finish, even with low-tack tapes.
If you must tape, do it over the blankets.

What about wrapping plastic?
Another alternative will be to wrap the piece in wrapping plastic. No tape is needed then.

overkill

.
Plastic provides zero protection. (unless it is raining)
Blanket wrapped and taped. -Bubble wrapped and plastic over
that if it is traveling to Mars...
Geez Louis, five blocks?
More likely to cause damage by moving it to the truck smacking a door jam.

As others have advised...
flat on its back on thick blankets on the floor of the van. No need to tie it or strap it in. If it should move enough to cause damage, it means you've got bigger problems than a busted piece of furniture. The heavy zig-zag quilted blankets, or pads, that the pros use are best. The flimsy ones that the rental places offer are next to useless unless you use enough layers to build adequate thickness. No need to remove the drawers unless you really need to reduce the weight for handling. Skip the plastic. Blanket-wrapping before handling is okay if you are facing tight quarters and doorways but, if necessary, do a neat, tight job of it and use plenty of plastic packing tape on the outside of the blankets and leave access to natural handholds unwrapped. If the forecast is for pouring rain, try to reschedule.
You may have been referring to stretch-wrap plastic film that the pros use over blankets when wrapping furniture. It works well for that purpose, but it helps to have experience with it and it's probably not worth the hassle for a novice on one piece. I wouldn't use it directly on the surface, though. When I was in the biz, we kept spools of wide cotton twill tape on hand for securing doors, fall fronts, etc.
Congrats on your purchase. It looks like a nice piece!

Tape over the blanket-- always a bad idea to tape the piece itself
I don't know where you live, but in NYC one could hire a dependable mover to carefully wrap it in a heavy padded blanket and deliver by truck for about $75.
Unless your husband and friend have experience moving large pieces of furniture, sometimes the cheapest solution is hiring a pro. Pros use professional padded blankets, packing tape, padded dollys, experience.
(Not to put a damper on your plan, but I've seen a lot of DIY moving jobs result in damage, just to save $50-75.)