Does the Army respond with "Aye, sir" to a command, or is that only for Marines and Navy? If not, what would their response be to a command?

As others have said, "Yes, Sir/Ma'am" is far more common - in fact, I don't know that I ever heard "Aye" while I was in. Sergeant through Sergeant First Class is "Sergeant"; Master Sergeant and above by rank. Warrant Officer 1 (WO1) is supposed to be "Mr./Ms./Mrs."... but that just seems a horribly awkward way to address someone in the military so they are usually addressed as "Chief" as with the higher Warrant Officers.

Hearing people say things like, "Roger, sir!" will sound just off-the-wall and bonkers... until you spend a while talking on radios and pick it up yourself.

Being a Navy brat, on my first day in basic training in 1973, I asked my drill sergeant if I could use the “head”. BIG MISTAKE. He told me in so many words that my head was on my shoulders but that the latrine was over there. Then he asked me my affiliation with the Navy? He then warned me to lose all nautical references such as deck, hatch and serveral other terms we usually affiliate with Navy or Marines, which I promptly flushed from my memory bank for the rest of basic training. Interestingly enough though, my previous exposure to the military was a determining factor for me being chosen as a squad leader, which I managed to hold for the duration of the cycle.

Along with the acceptable responses to orders in the Army already noted such as Yes sir, Roger sir are Hooah sir and Affirmative sir, Good Copy sir, Message recieved sir.

"Aye, sir" isn't used much in the Army. I catch myself saying it every now and then since I was an enlisted Marine at one time and old habits die hard. Instead, my typical response to a command is "Yes sir" or "Roger sir".