As I taxied past some Southwest 737s during a recent trip I saw what appeared to be different angles of the winglets relative to the wing. Are winglets adjustable, are they arranged differently from Port to Starboard, or is it an optical illusion?
Winglets are fixed to the ends of the aircraft. As can be seen below, the winglet has no movable parts and is fixed to the end of the wings.
Boeing 737 winglet; image from sae.org
What you'd seen is an optical illusion. The port and starboard side winglets would not be much different, usually (except that they are mirror images externally).
Interestingly though, Boeing has filed a patent for an adjustable winglet. Airbus is also working on a similar project, called the morphlet.Both of these are geared towards reducing drag and saving fuel.
All winglets are permanently fixed to the wings and are not adjustable.
737 winglets are not, to my knowledge, adjustable. However, some aircraft do have adjustable winglets, like the XB-70
737 winglets are not adjustable. There are several configurations in the fleet, as noted by @TomMcW, but they are all fixed. Airbus and other commercial aircraft winglets are also fixed. The only winglets with control actuation I've seen in actual use are on "flying wing" configurations like the Swift:
Studies (e.g. AIAA 2003-4069) show that for classic (tube-and-wing) aircraft, incorporating control deflections into an otherwise optimized winglet reduces the best lift to drag ratio.
No. The winglet is a fixed structure.