The song that Derek sings when they're waiting for Little Richard to show up is "It's Only a Paper Moon".
After Jesse says that Little Richard put the whop bop b-luma in the b-lop bam bom, this references Little Richard's popular 1957 song "Tutti Frutti." "Tutti Frutti" would later be featured in Mary-Kate and Ashley's movie "It Takes Two."
Steve only appeared briefly at the end where he's sitting in a booth at the Smash Club and has no dialogue.
At the Smash Club, after Little Richard and everyone else performs, Mrs. Carruthers mentions that she looked at the PTA rules the night before and found a rule that disqualifies Joey. So she wasted everyone's time at the Smash Club.
The song that Danny, Jesse, and Joey sing is "Where or When," a show tune from the 1937 Rodgers and Hart musical Babes in Arms.