USB = Universal *SERIAL* Bus. Data can only flow in 1 direction at a time and the USB pipe is small. you can purchase USB adapters for all the drives and run them on USB, but it will be slow going.
Internal IDE controllers are cheap and can be found used by the bucket load (check computer recycling centers, shops that sell off customers old parts after upgrades, etc.)
Internal SATA controllers can be found dirt cheap and is the best way to do what you are trying to do.
esata is an option, but not the direction you want to go as it's pricey.
Another option; find the cheapest used POS garage sale throw away computer you can find, and turn it into a cheap network attached storage solution. (Xubuntu is your friend.)