To quote Wikipedia:
Two commonly used languages that support many kinds of implicit conversion are C and C++, and it is sometimes claimed that these are weakly typed languages. However, others argue that these languages place enough restrictions on how operands of different types can be mixed, that the two should be regarded as strongly typed languages.
Is there a more definitive answer?
"Strongly typed" and "weakly typed" are terms that have no widely agreed-upon technical meaning. Terms that do have a well-defined meaning are
Dynamically typed means that types are attached to values at run time, and an attempt to mix values of different types may cause a "run-time type error". For example, if in Scheme you attempt to add one to true by writing (+ 1 #t) this will cause an error. You encounter the error only if you attempt to execute the offending code.
Statically typed means that types are checked at compile time, and a program that does not have a static type is rejected by the compiler. For example, if in ML you attempt to add one to true by writing 1 + true, the program will be rejected with a (probably cryptic) error message. You always get the error even if the code might never be executed.
Different people prefer different systems according in part to how much they value flexibility and how much they worry about run-time errors.
Sometimes "strongly typed" is used loosely to mean "statically typed", and "weakly typed" is used incorrectly to mean "dynamically typed". A better use for the term "strongly typed" is that "you cannot work around or subvert the type system", whereas "weakly typed" means "there are loopholes in the type system". Perversely, most languages with static type systems have loopholes, while many languages with dynamic type systems have no loopholes.
None of these terms are connected in any way with the number of implicit conversions available in a language.
If you want to talk precisely about programming languages, it is best to avoid the terms "strongly typed" and "weakly typed". I would say that C is a language that is statically typed but that has a lot of loopholes. One loophole is that you can freely cast any pointer type to any other pointer type. You can also create a loophole between any two types of your choice by declaring a C union that has two members, one for each of the types in question.
I have written more about static and dynamic typing at why-interpreted-langs-are-mostly-ducktyped-while-compiled-have-strong-typing.