Twerp's first adventure is with the Smokeys, devilish wisps of smoke bent on dominating mankind, that he manages to outwit with the help of his science teacher and a leading ecologist.
His second is with rag dolls, and specifically with an infernal one named Mourag, that he gets involved with when he goes to stay with his aunt Gwen in Connecticut. It causes such havoc before it is eliminated that it almost brings our Western civilization to its knees.
Twep's third adventure is with the Nethites, totally flat aliens from a planet stuck in a 'black hole', that want our scientists' help to get out of it and recover their lost dimension, threatening otherwisse to take over our planet. Largely thanks to his gift of ubiquity, Twerp is able to obviate this.
Involved in these adventures are also a ruthless bamboozling businessman, a wealthy American couple, Cabinet Ministers, a hoard of SCHs (if you want to know what they are, just read the first episode) astrophysicists, even a Nobel Prize winner, and of course those Smokeys, rag dolls and Nethites that Twerp has to contend with.