So, when you vomit, my EO books recommend rubbing ginger essential oil on your tummy, and smelling lavendar and peppermint to soothe your system. Those are nice, and I actually recommend putting a bit of peppermint oil in a spray bottle with a lot of water, to spray on your tongue and cool down your mouth when you've been puking bile.
However, the only thing I've found that actually resets my sensitive stomach so that I can STOP vomiting, and start replenishing my electrolytes and fluids, is flat soda pop. Really. I mix about half a cup of seven-up or sprite (flat) into half a cup of water, and take about a sip a minute, and my whole system calms down, and nothing comes up again for a while. Now I can't go straight from that to having meals or gulping down water-- but at least I don't end up in the emergency room for dehydration and continued dry-heaving (when you vomit but there's nothing left to bring up).
It's the only time I drink pop. But, better still, don't get food poisoning in the first place. Be smart, carry lemon EO for your water, and travel well.