In the last decade or so we've really been hit by Argentine ants around here. They don't really sting, but will bite if mashed between the fold of your arm or between your shirt or skin. The problem is their numbers are massive and in a vegetable garden cause big problems because they farm aphids on a Texas-size scale.<sigh>
Wallyworld and other places sell a gallon jug of "Ortho Home Defense Insect Killer". Spraying the legs of tables or the sides of pots does a really good job for me at keeping the ants away. It seems to last through a couple of rains, too. I started putting some potted vegetables on foam pads and spraying the pads...worked great, too! Naturally, it'll also keep other insects from crawling up the legs/pot sides. Not exactly an organic approach, but invasive ants aren't organic...they're evil aliens!
ETA: I get the jug with the battery-operated sprayer. It works well for me. In the past when I've ran out I got a jug with the manual pump and just switched the battery pump over to the new jug (the manual pump jug is cheaper