Hank says he wants to go on tour with Willie Nelson, cut an album, and open a chicken franchise. The latter is most likely a reference to Kenny Rogers, who opened a restaurant chain called Kenny Rogers' Roasters. The chain no longer exists in America, but oddly enough, still exists in Malaysia and the Philippines.
The man that Boomhauer is talking to, who speaks similarly to him, is supposed to be Bob Dylan who has toured with Willie Nelson.
Willie's doorbell ringtone is "On the Road Again."
When Hank gets to Willie's house, he walks by a guy and says "out of my way, Rooster Boy." It is supposed to be Lyle Lovett.
The song Hank sings that he wrote about Peggy is to the tune (and some of the same lyrics) of Buddy Holly's hit "Peggy Sue."