|Do you know where your variables are?|
The lazy answer is that these are all Turing complete programming languages, and can thus (skipping a few implicational steps) emulate each other. So yes, you are correct that given any Turing complete programming language, we can do object-oriented programming in it. Since all implementations of programming languages run on a computer, ultimately what you are doing is functional/imperative/logical/object-oriented programming in machine language.
However, it's a separate thing to ask if the syntax and semantics of a programming language makes one paradigm easier or harder than the other. I find programming languages such as Scheme much easier to work with exactly due to minimalistic core features and closures: if I want objects, I'll just wrap the methods in a closure. Doing the reverse in, say Java, that is, using classes and objects to emulate closures entails creating a new class definition for each closure you use, then instantiating objects from them.
Both are possible approaches, and as has probably been discussed in the monastery many times (sorry, I can't search right now), closures and classes/objects are just about equivalent. Now, many "functional" programming languages support objects (since it's really easy to do with closures) and many "object-oriented" programming languages support closures. Arguing which one is better is a source of much heat but usually little light.
As for me, I'm prone to pick a programming language that has closures rather than one that only has objects, because I tend to use closures more.
In reply to Re^3: I dislike object-oriented programming in general