Do you require some special license of permit to legally sell over the counter supplements on ebay?

Diet supplements are not regulated in any way.

this is an area where you run afoul of the laws for different states. Some states control some over the counter supplements, some don't. Sell to someone in the wrong state and you get a warrant issued for violating state pharmaceutical laws.

OTC ephedrine cold remedy, weight loss, etc. is a good example. Oregon requires a doctors prescription to purchase. Arizona doesn't.

I wouldn’t suggest anyone to become a seller on eBay. The most important thing you need to know is: 1) eBay does a very poor job to enforce winning bidder to honor their bids. 2) you are always the last person who gets paid. First of all, you need to pay eBay insertion fee and final value fee. FVF only applies if your item is successfully sold. Second of all, you will be charge a PayPal transaction fee for payment processing service. Then you need to pay USPS, UPS, or DHL to deliver the item to the buyer. The left over amount, minus your cost and 15% of government tax, will be the actual amount that goes into your pocket.
Although eBay claim your item might be eligible for an insertion fee credit if your item didn’t sell or the winner didn’t honor the bid. However, you can only use it once. In order to be eligible for the insertion fee credit if your winner didn’t pay, you will need to first of all file an Unpaid Item dispute on the 8th day after the auction ended. Then you’ll have to wait another week for the winner to response. If the winner didn’t response, then you can relist your item and get your insertion fee credit when your item is sold the second time. However, if the Non Paying Bidder reply to eBay says they want to complete the transaction, then you’ll lose the eligibility EVEN THOUGH THEY STILL HAVEN’T PAY YOU.
Remember, never ever use the “Sell Similar” feature even you have like 100 identical items because once you list your item through “Sell Similar”, you’re consider relisting your item and you are automatically not eligible for insertion fee credit. Tricky huh?
The most stressful part is their feedback system. Sometimes, there are sick people out there, they bid on your item just to mess around. Some even leave you a negative feedback just for fun. eBay will not do anything to remove it. Even though you think you’re undeserved, eBay will not remove it unless they are presented with a valid court order stating that the comment is slanderous, libelous, defamatory or otherwise illegal. eBay doesn't remove Feedback without a court order, even if a member believes it is retaliatory, false, unfair, or harmful to his or her name, character, or reputation.
But these are nothing compares to their new feedback policy starting in May 2008. Sellers are no long able to leave negative feedback for bidder. Sellers can only leave positive feedback. Yup! Even the winner doesn’t pay; you still cannot leave negative feedback to him or her. The seller will have no way to find out the credibility of the bidder.
Sometimes if eBay thinks your shipping charge is unreasonable, your listing will be removed without prior notice.
Also, if you’re new to PayPal, even thought you shipped your item to your buyer, PayPal will hold your fund for 21 days. That’s right, you won’t get paid for 3 weeks even though you have to pay your vendor, the shipping cost, and all the fees that listed above. Here’s the stupid rule that makes new seller’s life in hell:

PayPal and eBay are working together to make payments for eBay items even safer. Because we want both buyers and sellers to feel confident about sending and receiving payments through PayPal, we may temporarily hold payments for items sold on eBay.
Make sure to ship the item right away, so you'll have access to the funds sooner. We'll release the hold in 21 days unless you receive a dispute, claim, chargeback, or reversal on the transaction subject to the hold. We may release the hold earlier if either of the following occurs:
• The buyer leaves you positive feedback on eBay.
• We confirm that the item was delivered.* We can confirm delivery if you ship the item with USPS, FedEx, or UPS and either use PayPal shipping labels or upload tracking information from the transaction details page. This applies to transactions within the United States.
Additional hold period
If you receive a dispute, claim, chargeback, or reversal on the transaction subject to the hold, we may hold the payment until the problem is resolved.
Learn more about the PayPal policy for payments holds on eBay items.

My opinion is, don’t do it. It’s not worth the time since you don’t make much and it’s very stressful.

There should be ..more ppl die from over the counter drugs then illegal ones.