How do we define the mirror image of a knot in general 3-manifolds How do we define the mirror image of a knot in general oriented 3-manifolds ? For instance for a knot in an irreducible integer homology sphere.

I don't think there can be a general definition. 
The reason there even exists a definition in $S^3$ is that there exists an orientation reversing homeomorphism $h:S^3 \to S^3$ and $h$ is unique up to isotopy; the mirror image of a knot $K \subset S^3$ is then $h(K)$. But there are many oriented 3-manifolds which have no orientation reversing homeomorphism, and many which have a non-unique orientation reversing homeomorphism, so this definition will not apply in general.
Perhaps there are special definitions. For instance, suppose $M$ is an oriented manifold and $K$ is a knot contained in an open ball $B \subset M$, then there is a kind of "local mirror" of $K$: the ball $B$ has a unique orientation reversing homeomorphism $h$ of $B$ up to isotopy and using it you can produce a mirror $h(K)$. This should be well-defined independent of the choice of $B$.
