Who, or what, is the strange love of Martha Ivers?

Possibly the 'love' is not a man but her strange and damaged expression of the emotion. She truly loves Sam but would have probably killed him at the end if she'd been sure that Walter would have backed her up.

She's obsessive and neurotic, it's unsurprising that even her finer emoitions are a little odd in there presentation.

The Strange Love of Martha Ivers is really her husband, Walter. Or maybe is a reference to Martha and her love-hate relationship with all the characters in the film.

Martha's 'strange love' refers to the neurotic love that has grown out of her feelings of emptiness. This need for love has led her to have a long series of lovers. Walter lists them off for Sam. 'a gymnasium instructor in Philadelphia with a muscle for a brain and tendency to insipid verse...a guy named Pete in Erie who smells of fish and sings...last year's greatest fullback [who] flunked [his] bar exam but...wanted to be an industrial engineer...a guy who came along to fix a tire so well [he] became a city-paid inspector.' When Sam returns to Iverstown, Martha doesn't even recognize his name at first. However, once she realizes who he is, she becomes certain that he is the one man she has always dreamed about, the one man who can fill that emptiness in her. It refers also to the 'strange love' she shares with her husband. Throughout the film, she wants only to get away from him but, when she feels betrayed by Sam, she fears that Walter will no longer stand by her.
IMDB FAQ

There was a film called The Strange Love of Molly Louvain in 1932. It's possible that they just copied the idea.