Please post a picture to help us visualize this situation.
For a concrete tank you can use mortar to seal arouind the inlet and outlet pipes so sewage does not leak out into the ground in the vicinity of the tank. But the clean out hatches are left sitting in place unsealed so it doesn't take tremendous effort to unstick them to lift them off.
In normal operation the septic tank remains about 80% full and the water level fluctuates upwards from time to time. Baffles are sometimes used instead of T shaped inlet and outlet pipes. The baffles need to be arranged so that the surface of the water in the vicinity of an outlet pipe pointing horizontally does not have floating grease and scum.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.
I'm thinking i must have a "T" pipe. It's white plastic and looks like a T, kinda. I've read about putting grout around it, but i was wondering if there was anything else i could do to seal it up. It would be hard to get that on it while it was wet with sewer. Could i just fill the hole back up with dirt and let that seal it off?