Using straw bales in gardening becoming more popular these days. After use in greenhouses for growing vegetables, straw bales can be spread around garden plants as mulch or used to prepare compost for soil fertility improving.
One of the best ways to start testing this "no soil method" to grow plants, is to try with tomato. As most probably already know, tomato has a large and strong root, and therefore able to absorb water easily. If you add on top of straw bales drip irrigation system, then mistakes are almost impossible. Straw bale growing is definitely worth trying.
*Photo by Giancarlo Dessì (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Common