what was the value? if $5,000 or more you need a certified appraisal. if you don't have one expect a letter from the IRS since the signed appraisal must be attached to your return (your return will need to be mailed) even if less you need documents recognizing the contributions. the moving costs are not deductible
In order to claim a tax deductible donation for a single item or “group of similar items“ of more than $5000, you must have a signed appraisal by a qualified appraiser, and you must mail the IRS a copy of form 8283 which is signed by both the appraiser and by a financially responsible official of the recipient organization.
The IRS is not specific on what a “group of similar items” means. However, if you were to try to group a large donation of used household items into smaller groups, such as “used furniture“, “used kitchen ware”, “used household accessories“, and so on, each less than $5000, but totaling more than $5000, that could certainly raise a red flag.
You can deduct out of pocket costs that you paid in connection with providing a service to a charity. If you donated the items to a charity, and you paid someone to pick them up from your house, and deliver them to the charity, then I think that would be separately deductible from the value of the items.