That'll be the theory answers taken care of, but the practice side seems to have been neglected...
Strong-typing means that you can't use one type of variable where another is expected (or have restrictions to doing so). Weak-typing means you can mix different types. In PHP for example, you can mix numbers and strings and PHP won't complain because it is a weakly-typed language.
$message = "You are visitor number ".$count;
If it was strongly typed, you'd have to convert $count from an integer to a string, usually with either with casting:
$message = "you are visitor number ".(string)$count;
...or a function:
$message = "you are visitor number ".strval($count);
As for which is better, that's subjective. Advocates of strong-typing will tell you that it will help you to avoid some bugs and/or errors and help communicate the purpose of a variable etc. They'll also tell you that advocates of weak-typing will call strong-typing "unnecessary language fluff that is rendered pointless by common sense", or something similar. As a card-carrying member of the weak-typing group, I'd have to say that they've got my number... but I have theirs too, and I can put it in a string :)
static functions are functions that are only visible to other functions in the same file (more precisely the same translation unit).
EDIT: For those who thought, that the author of the questions meant a 'class method': As the question is tagged C he means a plain old C function. For (C++/Java/...) class methods, static means that this method can be called on the class itself, no instance of that class necessary.
Best Answer
Static/Dynamic Typing is about when type information is acquired (Either at compile time or at runtime)
Strong/Weak Typing is about how strictly types are distinguished (e.g. whether the language tries to do an implicit conversion from strings to numbers).
See the wiki-page for more detailed information.