Let $X$ be your favorite undecidable set of primes.  In a language with one unary function symbol, say f^p(x) = x iff $p$ is in $X$  and also that there is a unique cycle of length $p$. Add that f is a bijection.  Now the prime model contains cycles of exactly the lengths in $X$ and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.