There are hundreds of ways to incorporate music into your improv. Start with these styles. Explore others. The is no one way to do this.
TIPS to RHYMING: While not all music has to rhyme, your audience almost always expects this skill. Most songs are comprised with rhyming lines of poetry. There are dozens of rhyme schemes (which lines rhyme with another). What ever the scheme, here is a simple rule to good rhyming on the spot.
1) As soon as you here the subject for the song, do a quick brainstorm of elements to that topic.
2) As you formulate a great idea, end with your first thought THEN figure a way to get there.
In our BLUES form (And there are many among Improv teams out there) each player takes a verse of four lines with rhyming pattern AABB. After each verse, a blues chorus, repeating the title 3-4 times, is sung in harmony (hopefully LMAO). The final verse, each player takes a line of a verse. Player one sets up player two for a rhyme. Likewise, player three sets up player four for a rhyme. (With three players, player one sings line one and four of the final verse).

