Do I have a choice to choose between reserve and IRR after active duty duration expired?

You are probably confusing "reserve component" with the "US Army Reserves".

When you first enlist with the military, you typically incur an eight year Military Service Obligation (MSO) that overlaps with your contract. When your enlistment contract completes, you still have to fulfill the remaining MSO, but you can do that in the reserve component and it can be in the IRR or one of the selected reserve components of the Service (in this case, the USAR or ARNG).

So, hypothetically, if you had a three-year enlistment, reenlist for another three years, then you still will have a two-year MSO which can be fulfilled in the USAR, ARNG or IRR (technically the IRR is part of the USAR, but it's often mentioned separately).

Your initial contract, regardless of how many years it is for, you owe 8 years. If you do but only x1 4 year contract, you still owe 4 additional years. You have two options. 1) Contact your Retention NCO and inform them that you want to finish out your remaining contract with the Reserves (or Guard). Come ETS from Active Duty, boom you're in the Reserves (or Guard) for 4 years. 2) Tell your Retention NCO that you are NOT re-enlisting Active Duty, nor do you want to go to the Reserves or National Guard. Upon ETS from Active Duty, you are scrolled onto the Roster of IRR Soldiers. Easy Peasy.

There is, however, another COA. You could transfer to the Reserves (or Guard), and then when you get to your unit, you could request transfer to the IRR. It's a tad more paperwork and you have include your Reserve Unit Commander AND Retention NCO into the process.

Regardless, your first step is to figure out what you want to do, then go visit your Retention NCO

You can join the reserves as long as you qualify. Speak to your retention NCO and if you are in the US contact the reserve recruiter in your area.