I have been told that a Wisteria Vine will kill the tree that it is growing on.

That's an issue I've been curious about. Certainly the stems have the potenial to choke another plant. When you look at wisteria trees or older vines on pergolas, the stems can be tightly wound around each other. Interestingly, the tightly wound stems merge into one to make very attractve gnarly branches and trunks. But that merging which clearly doesn't result in choking, would only happen with the wisteria itself I'm sure. But, in its native habitats, wisteria grows scrambling over rocks and up trees and shrubs. And it apparently does it without killing the plants it uses for supports. There's a large 'wild' garden in the Niagara area that has a large collection of wisterias that it lets run wild into the trees. According to the owner, the wisterias do not kill the trees and I didn't see many/any dead trees with wisteria on them during several visits there over the years. Still, I suspect younger trees with smaller girths could easily be 'strangled' by a stem tightly winding around it - or simply by being overwhelmed by the weight/volume of the vine.

I wouldn't risk making a mess of the oak by training the wisteria into it. I'd prune the wisteria to make it a stand-alone tree itself (although it sounds like the wisteria is trying to reach for the light so it's not happy there.) If you want to fill in under the oak for some reason, make a woodland garden under it. But oaks are majestic trees on their own and really don't need much in the way of companions. Add a nice bench and make a seating area under it to enjoy the shade!

If you decide to move the wisteria to a spot that has more sun and will make it happier, consider planting a climbing hydrangea to cover the trunk of your oak. I will climb the tree trunk on its own and will be happy in the shade of the tree. It will take a few years to get established and start blooming (mine first bloomed at 5 years) but is a great plant that will do what you want the wisteria to do. There are a few varieties with ornamental leaves as well.

Here is a link that talks about shrub and vining hydrangeas with variegated leaves. Near the bottom there are photos of several variegated hydrangea vines.

Here is a link that might be useful: variegated hydrangea vines