Colleague stole my work and is publishing it as his own; my PhD supervisor supports him; I got the paper to review. How to proceed? By chance, I am reviewing now the paper which I recognised as a paper of my colleague. We are from the same institution and I am surprised that I got this paper to review, but, on the other hand, I am lucky to see it before it's published.  My colleague mentions in this paper the methodology like it was his idea but actually, I am the one that developed it, made it work and applied it,  together with the help of my supervisor. In short, he wants to be the author of the idea and the methodology. This is, in fact, what comes out from the paper.

I am now preparing my own paper about this methodology and my work, and I don’t have any publication on it, so far, just a poster from when I participated at a conference six months ago.

I talked to him about it but he doesn’t feel that it is wrong or ethically incorrect.

On top of that, we have the same supervisor. I talked with him as well, and he was threatening me, in a political correct way. He claims that it is okay, and in my paper, I will have just to cite their work in the introduction. He also stated that my work has a different approach in a small detail, so I will criticise their method and put mine as the better one. However, it isn’t true, because my approach is based on the methodology mentioned in the paper which I am reviewing now.

I really don’t know what to do. I was thinking to not review the paper, but it doesn’t solve the problem. If I reject it, I will have to write the reason why I am doing that, and it may turn my supervisor against me. 

I would like to act in the most appropriate and ethically correct way. Just don’t know how. I would be grateful for all insights.
You shouldn't even think about it, do not review that paper, it's a clear conflict of interest, even more because the author is your direct colleague. And the only solution is to sit all together and explain to them that your contribution to said article is significant and you would like to be a co-author. If they have problems with you being a co-author and you have done substantial work then I would seriously consider if you want to be in this research group.