I was given to review a journal paper that overlaps with a submitted paper of ours I was recently given to review a journal paper that significantly overlaps with a work that we recently submitted to a conference (about half of the contributions are the same).

Any advice on what to do in this case?

(even if I tell the editor now that I'm unable to review the paper, I've already read it).
If you already submitted the paper you have some evidence of your own work even without a "published" preprint. Inform the editor of the situation and get advice. You may even be permitted to review it and point to your own paper in the review, but that would be up to the editor. 

Parallel independent work is pretty common, especially in popular fields. 

One option is to use editors of the two journals (assuming there are two) to act as intermediaries to get the two groups together. I don't think I'd recommend doing it on your own, however.