When cooking soup, I do not like the taste that olive oil imparts...?!

You don't have to use olive oil or any oil.

I make really good soup, its easy and cheap and its how restaurants do it ....you start off with scraps, clean vegetable peels, turkey carcass, bones and pan drippings for meat stock, water that you cooked shrimp and clams in for fish stock plus all the shells, you just cook scraps a couple of hours and you'll be amazed at how great the stock gets before you even start your soup.. You then strain out and discard all the stuff you used and put in the cooked meat and chopped veggies you had peeled.
The best broth makes the best soup.

You can get by with out using olive oil and butter.

I use an ordinary oil, just a little to be able to fry off the main three veggies to get them to release their flavours and tastes and add some water and give a good boil. Carrots, onions and Celery or Leeks.

Lamb or Pork Shanks, Beef Bones, Ox Tail Bones Lamb Neck chops thoroughly browned and then simmered in water will give great tastes. Chicken could be used also.
Allow to cool and when they can be handled remove the meat from the bones.
Allow the water to cool and remove the fat.
Add the veggie stock. The good boil will draw out most of the goodness from the veggies. They can be used or discarded.

Use chicken and pull the skin off first. I use diced carrots, celery, onions, basil, salt to taste. You don't have to use oil in soup. Throw your veggies in raw. Don't saute them in oil first. No need to.