No preservative is needed in an anhydrous (no water) body oil. Christa's recipe (post #10) and your mom's olive oil are anhydrous.
Zany's blend of oil, polysorbate, and vodka would need a preservative unless the total alcohol content by volume (ABV) is 20% or higher, as she already explained.
I've had mixed results using polysorbate as a solubilizer, even PS 80. It's fine if you're solubilizing a small amount of essential oil in a lot of vodka, like you would for a scented spray for linens, room air, or as a body spritz. But I'm not so convinced it works that well in a product with a higher percentage of regular carrier oils, as I'd want for a body oil product.
In my experience, I've had to use a lot more PS 80 in proportion to the amount of carrier oil to get the vodka and carrier oil to solubilize properly. When the PS 80 content gets that high, I question why I'm bothering -- the mixture is way more PS 80 than oil, and that's not what I want.