Dave Elledge, owner of P.I. Audio, recommends Triode Wire Labs power cords for his BUSS line of products. Most BUSS owners utilize the "Seven Plus" or the High Power "Digital American" power cords; a few have the top of the line "Obsession" and "Silver Statement" power cords with superb results. The key here is synergy. The use of Triode Wire Labs power cords coupled to many power conditioners, such as the UberBUSS, provide a splendid integration of elements that when combined produce a total effect that is greater than the sum of the individual components. Simply put, they work very well together.
Many have found similar synergistic results with power regenerators (PS Audio, Isotek, APC, etc.) and other types of power conditioners (Furman, BPT, Torus, Bybee, Shunyata, etc.)...
To answer you original question, if only using one TWL power cord, I would recommend your Option #1, to "Plug the Triode Wire Labs power cable into the wall and plug the power strip on its end" for the best results.
Your other question was "Or does having a power strip anywhere in the chain obliterate the benefits of using any Triode Wire Labs cable?" ... I have numerous customers, especially in Europe, that utilize "power bars / power strips" with magnificent (at least they tell me) results. In Europe, with Schuko-style mains connectors, they are usually limited in the amount of receptacles available. Also, the better designed & higher quality "power bars / power strips" will sound better...
My $0.02,
Pete