Cut an "X" shape on the top and bottom of each tomato. This makes peeling the skin off the tomato easier.
Bring two quarts of water to a boil and drop a few tomatoes at a time into the boiling water. Leave them in the water for about 15 seconds, and remove them from the water. This process is called blanching, and makes it easier to remove the tomatoes skin.
Sit the tomatoes on a large tray and let them cool for a few minutes. Peel the tomatoes by pinching the skin at the top where you cut the X shape and pulling the skin off.
Cut out the core, or center, of the tomatoes, or cut the tomatoes into quarters. Place the tomatoes into a large bowl and refrigerate.
Peel and chop the onions, core and chop the bell peppers, mince the garlic, and chop the fresh oregano. Put the chopped ingredients in a medium-sized bowl and set aside.
Heat up a deep iron skillet on medium-high with olive oil. Put all the ingredients from the bowl into the iron skillet and cook until the onions and the peppers are tender.
Add all of the tomatoes, sugar and vinegar to the iron skillet. Cook on medium-low for about a half hour. Remove from heat.
Wash the canning jars in hot, soapy water, and rinse thoroughly. Let the jars dry.
Fill the canning pot almost full with water, and bring the water to a boil. Clean and sterilize the quart-sized canning jars by dipping each jar into boiling water for one minute. Turn off the heat after dipping all the jars. Drain off the excess water in each jar, and dry the jars.
Fill each jar with tomato mixture while the jars are still warm. Leave 1/2 inch of space at the top of the jar.
Add 1 teaspoon of salt to each of the jars, and wipe off any excess tomato mixture from the rim with a damp paper towel or dishcloth. Put the lids on each jar, put the bands on and tighten the bands. Turn the bands until they are on securely, but not tight.
Lay a towel on a flat surface. Place a second towel on top. When you take the canning jars out of the pot, you will place them on the towels until they cool.
Put the canning jars in the canning pot water. Turn the stove on medium-high, and bring the water to a boil.
Boil the water for 40 minutes, and remove the canning pot from the heat. Remove the canning jars from the pot, using a canning-jar lifter.
Pick up each jar with potholders. Tighten the band on the jar, and turn the jar upside down on top of the towels. Flipping the jars upside down ensures proper sealing by forcing all the heat inside the jars against the seals. Let the jars sit overnight before storing the Italian tomatoes in a dry, cool area.