What are the major duties of an Operations Sergeant?

The list of possibilities is longer than I could post.

But reality is an ops Sgt is doing what the CDr and 1SG don't have time for.

It could be anything for reviewing awards and SM actions before they get them
To the more common training records processing

IOW the ops Sgt job is what ever the CD-R and 1SG priorities and needs are so go ask them, they are the only ones that can answer the question

Look at OPS as your S1/S3. Mine processes all actions awards, UCMJ, flags, leaves, passes etc. I manage the rating scheme and since the Army went to EES for NCOERs they have been cut out of the NCOER process. I know some 1SG will have their OPS manage APFT failures and the ABCP as well but I am kore comfortable taking care of those myself. Drafting any correspondence for the commander and I also falls on their lap.

As you can see it is very important to choose your OPS and Training Room personnel carefully. It sucks pulling good Soldiers and NCOs off line but it is a must if you want the company to be successful

I obviously was never a 1SG, but I did serve as the Training NCO for the HHT and a tank company. Both while deployed and in garrison. In addition to my normal duties to roll out in the commander's vehicle as his gunner, my responsibilities as the T. NCO included, but we're not limited to: daily perstat monitoring, persdat maintaining, updating and dissemination of the Training calendar or mission schedules, any and all paperwork processing to high such as awards, UCMJ, NCOERs and OERs, etc, active roll in briefing PSGs of requirements of their soldiers (ie medpros, appts, schools), process and track leave during deployments, process out SMs under chapter if necessary, the list goes on and on. I actually received an AAM for a PersDat system I developed in excel. It eventually was adopted by many of my counterparts throughout the squadron.