gifts
You can give a gift of any value to someone else for business. HOWEVER the tax law says the maximum total value of gifts that can be given to one person in a year and DEDUCTED on the tax return is $25. That low limit was set years ago -- back when $25 meant something -- and has never been adjusted for inflation etc.
If given to an employee then you can add the excess into the W-2 and it would be treated as compensation and fully deducted.
If to a client you just give it to them and limit the deduction to $25 on your tax return.
As for company policies against accepting gifts -- that is a company by company issue and not an IRS issue.
If you do something like a nice gift basket to an office you should not have an issue with the IRS on the deductibility.