Strong typing probably means that variables have a well-defined type and that there are strict rules about combining variables of different types in expressions. For example, if A is an integer and B is a float, then the strict rule about A+B might be that A is cast to a float and the result returned as a float. If A is an integer and B is a string, then the strict rule might be that A+B is not valid.
Static typing probably means that types are assigned at compile time (or its equivalent for non-compiled languages) and cannot change during program execution.
Note that these classifications are not mutually exclusive, indeed I would expect them to occur together frequently. Many strongly-typed languages are also statically-typed.
And note that when I use the word 'probably' it is because there are no universally accepted definitions of these terms. As you will already have seen from the answers so far.