Does massaging a pregnant tummy with oil several times a day really prevent stretch marks?

It helps. There are many safe commercial products that contain lanolin or oil for helping pregnant abdomens avoid elastic skin breakdowns also known as "stretch marks.".
Stretch marks. I have seen a number of pregnant patients develop a contact dermatitis using cocoa butter containing creams. Doesn't happen with everyone but I have seen it and i always ask such pts. Something to consider.