You will have to get SMS to get you the International Rates Desk to price the itinerary when another carrier is involved in one of the segments. Was the DL agent you talked to who was unable to get you beyond STR a regular SMS agent or someone from the Rates desk?
Basically, s/he needs to be looking for an M fare from OKC to ZRH, not OKC to STR. Most of these higher fare categories (M, B, Y) allow "interlining" with another carrier on a part of the journey (in your case, another carrier between Germany and ZRH). The M fare between OKC and ZRH doesn't seem to allow interlining with NW, UA, LH, and some others though LX (Swiss) didn't seem to be excluded. I believe that the M fare you want is an "MAB2" fare.
After s/he determines that LX is a possible combination on this fare, the next trick is to look for the corresponding booking class/inventory on the LX flight that is "compatible" with the DL "M" fare. In most cases, the LX portion will be booked in one of their lowest Y classes (e.g., E, T, W, or L, etc., for LX). Exactly which LX class it is that entitles a combination with a DL "M" fare, I am not sure (hence my question above to
rcs85551)
Hope this wasn't TOO confusing...
