I've been looking for methods like Mann Whitney, but without homogeneity of variance. So far, I found that I suppose to test for stochastic dominance instead - i.e. modifying the null hypothesis. Could anybody refer books or any literature for me to study further? Thanks.
First, let me point out that Mann-Whitney does not test stochastic dominance. It tests the null hypothesis $P(X > Y) = P(X < Y)$. If $X$ is uniform on $[0,1]$ and $Y$ is 1 with probability 0.9 and 0 with probability 0.1, then the null is false but neither variable stochastically dominates the other. Stochastic dominance is a stronger condition.
There's plenty of literature on testing for dominance, though it is highly technical and requires some understanding of empirical processes. A Google Scholar search for "test stochastic dominance" will work. A famous reference is, e.g., Barrett and Donald (2003), Econometrica, 71, 1, "Consistent Tests for Stochastic Dominance".