Strawberries are ground hugging plants with runners (long tendril like stems with baby plants on the ends that will root when they touch ground. So they can't be grown "vertically" unless you provide soil for them to grow in. But since they are shallow rooted, there are several vertical container planting possibilities.
One DIY I'm thinking of trying is using shipping pallets (line with landscape or burlap cloth, fill with potting mix, plant between slats through slits cut in the cloth, allow them to root and establish, then stand up the pallet on one end.
They also SELL "strawberry planting bag" and "strawberry tower" as well as the classic "strawberry jar".