The walnut table I just finished has one coat of oil based Varathane polyurethane. In caring for it in the future, is wood oil or any such care product of use, or will it just float and muddy the surface?
OK first off one coat of oil-based poly probably isn't enough, but it does depend on what use the piece is put to how much finish does constitute an adequate protective coat. For furniture that sees regular use, handling or wear two full-strength coats should probably be thought of as the minimum necessary for protection (4-6 coats if you're diluting and wiping the finish on).
In caring for it in the future, is wood oil or any such care product of use, or will it just float and muddy the surface?
They are of use in that they can help clean off dust and grime*, and when the finish has dulled they add sheen ....as long as they remain on the surface, but, they're not actually any good for the wood. All manufacturer's claims about how they care for your furniture can be lumped together as hogwash >_<
How should we care for finished furniture?
The primary care step should be regular dry dusting, with wiping using a damp cloth reserved for when the surface is actually dirty (because it is water that will do most to undermine a finish over the years, eventually doing more harm than dust or grime).
Other than dusting the oldest way to care for finished wood I think was waxing and it's still the best option in many ways. Any decent paste wax (like Johnson's venerable Paste Wax in the yellow tins) is a much better option than any spray "furniture polish" that contains oils or silicone.
Note you can easily make your own paste wax at home if you prefer, brief instructions at the end of this Answer.
*But so can a cloth dampened with warm soapy water.
For woodworkers and anyone else who routinely has some mineral spirits (UK: white spirit) or turpentine in the house if a piece gets actually greasy on a regular basis it's much better to degrease the surface with one of these solvents than it is to wash it down with soap and water, it won't harm the finish and you don't risk water getting through to the wood and undermining the finish, particularly at edges or anywhere else it is thin, worn away or otherwise damaged.