Wade's line "I'm a duck not the Wichita lineman!" is a reference to both Bones' catchphrase on 'Star Trek' ("I'm a Doctor, not a _____!") and to the popular song "Wichita Lineman."
In the "Swine Trek" segment, Booker wears a Russian costume and speaks Russian, while Roy appears to be wearing a martial arts outfit. This is in reference to the Russian and Japanese characters from the original 'Star Trek,' Chekhov and Sulu.
The repeated "Don't call me Shirley" joke is from the popular spoof movie 'Airplane!'
As the captain in the "Swine Trek" segment, Orson wears a toupee, a reference to the hairpiece worn by William Shatner as Captain Kirk in the original 'Star Trek.'