Okay, so I was only able to pull off two of them. My tongue isn't as athletic as Inna's, but here's my rendition of the tongue-twisters anyways:
Карл у Клары укpал кораллы, а Клара у Карла украла кларнет.
Karl stole corals from Klara, and Klara stole a clarinet from Karl.
Шла Саша по шоссе и сосала сушку
Sasha walked down the highway and sucked on a dry (ring-shaped) cracker.