Tax Year Prior to 2020: A company lost most of my belongings during my PCS move. They aren't reimbursing me for the full amount. Can I claim the losses? I planned on selling most of the items.

Maybe.  You will want to wait until the final decision is made if they are personal belongings.  That said, if you planned on selling them, and you have a business, the cost you paid for those items (minus reimbursement) can be deducted as a normal business expense on your Schedule C.

If they are your own personal belongings, you could try to claim a Casualty/Theft loss. When you lose an item due to an accident, theft, or act of nature, you may have a tax deduction for the value of the property that is not covered by your insurance (or reimbursed).

The software will walk you through it, but here is how it works: Individuals are required to claim their casualty and theft losses as an itemized deduction on Form 1040, Schedule A Itemized Deductions. 

1. For property held by you for personal use, Subtracted any salvage value (zero for theft) and any insurance or other reimbursement from the loss amount.
2. Then, subtract $100 from each casualty or theft event that occurred during the year. 
3. Then, take that amount and subtract 10% of your adjusted gross income from that total to calculate your allowable casualty and theft losses for the year.
4. That's the amount that goes on your Schedule A Itemized Deductions.

If your property is personal-use property or is not completely destroyed, the amount of your casualty loss is the lesser of:

• The adjusted basis of your property, or
• The decrease in fair market value of your property as a result of the casualty

More details can be found at this link  http://www.irs.gov/taxtopics/tc515.html

That said, the amount would have to be pretty large for you to be able benefit.  Also, you must file Schedule A as I stated above.  But, if you want to give it a shot in the Casualty and Theft section of the software, it wouldn't hurt.

How to enter it into TurboTax: While inside the software and working on your return, type casualty loss in the Search at the top of the screen (you may see a magnifying glass there).  There will be a popup that says Jump to casualty loss.  Select that to get to the general area. 

Unfortunately I don't have a business. I planned on selling the items at conventions and later on the internet. Does that change the situation completely?