Anyone is quite a flexible pronoun. It can be translated as jeder in substantival meaning (in place of a noun). As jeder it means no one special. If anyone is used to describe one person that is at the point of speaking unknown then it should be translated with irgendjemand (also in place of a noun).

Das ist nichts besonderes, jeder könnte das. = This is nothing special, anyone could do it.
Du kannst jeden fragen, keiner wird es dir sagen. = You can ask anyone, nobody will tell you.
Jeder kann lernen, Auto zu fahren. = Anyone can learn to drive a car.

Hat irgendjemand meine Katze gesehen? = Has anyone seen my cat?
Warum würde irgendjemand so etwas tun wollen? = Why would anyone want to do this?

With somebody we mean one certain person that is either unknown or not defined more closely. It is translated to jemand (substantival use) or irgendjemand (also in substantival use) if you want to stress the fact that it doesn't really matter who it is. Irgendwer can actually be used the same way like irgendjemand.

If we say anybody (irgendwer / irgendwen) we put an emphasis on the fact that there is a person, about which we don't know anything in particular. If we compare the following phrases, we will see that there is a difference between jemand and irgendjemand (even though, it is hard to translate this subtle difference.)

Jemand könnte Gitarre spielen = Somebody could play the guitar.
Irgendjemand könnte Eier kaufen. = Somebody could buy eggs.
Ich denke, irgendjemand weiß es. = I think somebody knows.
Ist irgendwer zu Hause? = Is there someone at home?