To harvest all of the vines you will need a berrycollector.
The most important recipe for most of the vines, is the crafting of a Bushel. The Strawberry Vine is the only vine that doesn't drop a vine, it drops strawberries (1-4).
The main purpose of the vines, is the crafting of the newly added food-types by the Soul Forest Mod. You can't craft the vines directly into food, you will first need to craft the vines into bushels as described above.
With Strawberry Bushel you can only create a Strawberry Pie.
The Strawberry Vine can be used as a farming material, if you would make a big "vine-farm" you can easily harvest more then enough of this vine to make a lot of Strawberry Pies. But ofcourse it can also be used to decorate the walls.