Have a look:
I bought some very healthy-looking strawberry plants recently. Some had runners on, which means I can get more plants from them. I have planted them in large pots, which I have stacked in a tower. This is how it looks:
I pushed a metal pole into the side of the bottom pot, then 'threaded' the other pots. The pots have three drainage holes spaced around the edge. There is plenty of room to add more pots as the runners grow. See the green pot on the left - it has a large runner growing in it. There is even a couple of strawberries already!