What is Java written in?

The answer to your question - What is Java written in is -No.

OCaml, Haskell, Lisp dialects like Scheme, and several other languages are often used in the development of hobby languages.

Many languages are implemented in C because it's a ubiquitous language, and compiler-writing tools like lexer-parser generators (such as yacc and bison) are well-understood and almost as ubiquitous.

But C itself couldn't originally be developed in C when it was first created. It was, in fact, originally developed using the B language. Earlier languages (like Fortran) were usually bootstrapped using a native assembly language or even machine code long before C ever existed.

Unrelatedly, language paradigms like OOP are generally language-agnostic. The functional paradigm, for example, was developed (by Alonzo Church) as a foundation of mathematics long before any programming language ever existed. The procedural and structured programming paradigms came out of the mathematical work of theorists like John von Neumann. Object-orientation was developed by several different and unrelated efforts, some out of the lambda calculus (the functional paradigm) and some out of dynamic programming systems like SmallTalk at Xerox PARC by Alan Kay.

C is merely a tiny part of the story, decades after these ideas came into being.