A Ring of Satiety (rare) can help prevent starvation. The Rogue class also suffers from hunger less than the Mage or Warrior. Likewise, the Warrior will regin a small amount of health when eating (which offsets the need to rest as often).
Otherwise, look for the dew drops that appear when walking through tall grass/mushroom/flower tiles. They will provide a small amount of HP.
An enchanted vampiric weapon will also regain some of your health when you strike with it.
The Mage's subclass: "Warlock" will have his hunger eased slightly, and wounds healed a little, with each enemy killed.
So, there are some ways. Also, it doesn't seem that Hunger causes any negative side effects, so I suggest you wait until you are Starving in order to ration out your food the most effectively. I usually wait until I am around 70% health before consuming the next ration, since being well-fed will replenish that health.
A well of healing will also remove hunger/starving status.
Also, while Mystery Meat will randomly cause a negative condition, you can burn it in fire trap or with Firebolt Wand to create "chargrilled steak" which has same nutritional value as previous, but without negative affect. This makes piranha's much more useful if they can be farmed safely (battle wands and boomerangs).