Joe,

XOs across the army have similar responsibilities.  The marginal differences come from your unit type, company HQ structure, and your commander’s needs and preferences.

That said, here’s my advice…

Get with other company XOs to help get yourself up to speed.  When she returns, maximize whatever time you get with the outgoing XO.
Is there a Company HQ SOP?  If so, is it being followed?
Spend time with the Ops NCO to understand the current personnel and admin systems in place.  How does your company HQ handle leave?  How does it track Soldier duty status?  Inbound Soldiers?  Is it effective AND efficient?
Spend time with the Training NCO to figure out the training management system your company/BN uses.  How far in advance do you need to plan and resource training?  What methods and systems are in place to ensure consistency and thoroughness for each training event?
Accompany the supply NCO and the Commander on a monthly inventory and sensitive items inventory.  Ask questions.  You will see how organized your company supply is, how well they know their job and systems, etc.
Get with the commander to see what all your job will entail.  XOs tend to fill admin and logistics roles for their companies, but some commanders add things, such as operations support or additional duties.  Get a full scope of your anticipated responsibilities and read relevant doctrine.

There are a lot of details in these, but it ought to be enough to cover your bases.  Good luck.

Shep