A strong type system is a type system that has a compile-time restriction or run-time feature that you find attractive.
A weak type system is a type system which lacks that restriction or feature.
Seriously, that's it. You read the Wikipedia page, so you know that there are at least eleven different mutually incompatible meanings of "strongly typed". The term is useless unless clarified; no two people discussing a type system need have the same definition in their heads of "strongly typed".
The sensible thing to do is therefore to avoid using "strong" and "weak" entirely; when you talk about a feature of a type system, simply describe the feature rather than characterizing it as "strong" or "weak". If you mean "I like languages where the compiler assigns static types to expressions and searches for type errors" then say that. If you mean "I like languages where every object has one or more associated data types and can describe those types reflectively at runtime" then say that. Don't say "strong" because someone will think you mean "statically typed" and someone will think you mean "has run-time reflection", and those two things have pretty much nothing to do with each other.
Keep in mind also that many people use "strong" to mean that a particular type system restriction is impossible to ignore, and some use "strong" to mean the opposite: that a restriction is encouraged but can be avoided. For example, someone who believes that a type system is "strong" if type errors are impossible at runtime would characterize C# as "weakly" typed, because C# allows the developer to insert type conversions that will fail at runtime. (example:
short x = (short)(object)(123.ToString());) Someone who believes that a type system is "strong" if it encourages writing programs where the compiler finds many but not all type errors at compile time would characterize C# as strongly typed for the same reason. If the same feature of the type system can be reasonably characterized as both "strong" and "weak" then we know that the terms are useless and should be avoided.