When I turn on the outdoor faucet, it sounds as if there is water spewing out behind the wall and I hear dripping sounds after I turn it off. While the water is on it runs as if oxygen is getting into the water line. What can I do to find out what is going on and how do I fix it?

How long have you left it open for the water to run out? It is possible you have air trapped in the lines. If your turning on the faucet from the outside and not from a remote location then there is no way for water to be gushing from anywhere but the location of the fawcet. Can you see any threads where it is attatched to the pipe?

The faucet is attached to the pipe via a clamp. I let the water from the faucet run long enough to water my strawberries (at least 5 minutes) on 10 different occasions over the past 2 weeks. Is it possible that it is the valve?

Mostly it depends on what is really happening to determine if it is the valve or not. Does the sound change if you run it without a hose connected ?

No. The sound does not change if I run it with a hose. However, when a nozzle is on the end of the hose and stops the flow of water in the hose, it sounds as if the water is still running. Like there is no nozzle at all.

Do you have a water softener hooked to your system or a bladder from a well pump ?

No we do not have anything hooked to our system except for the smart meter the water company recently put on and this faucet is not in the same area.

Is this a frost proof hose bib and did you leave a hose connected to it last winter?

Yes it is frost proof and yes I disconnected the hose for winter.

Sounds like hose bib has rupture inside, after the point at which the stem shuts off the water. This is typically cause by leaving a hose connected during winter months. With a hose attach, the water in the hose bib cannot drain, freezes and ruptures the hose bib.

Replace hose bib.