WY company selling from NJ location
The question is: do I need to register a foreign corporation in NJ (where the products are warehoused) if incorporated in WY, and, do I need to file annual corp tax return?
This is one very clear picture of a business, thank you.
First let me answer the question about tax return. All legal entities in the US are required to file annual tax return with the IRS, so your LLC is not an exception. You will also need to file Annual Report in Wyoming, but its a relatively simple and inexpensive process.
Now to your question about registering a foreign entity in New Jersey. I will start from a quick disclaimer: since the question of foreign registration always comes with plenty of question marks it is highly recommended that you consult with a professional corporate attorney or a CPA that has good understanding of interstate taxation and other related laws. I will give you my version which you can use as a reference for further research.
As far as I understand, your company doesn't have any real physical presence in New Jersey, and you happen to use a third party in this state (contractor) to do your shipping fulfillments. As such it seems like your business activity in New Jersey does not fall under the definition "doing business" in this state, so I believe you are not required to register your company in that state.
With that being said, the fact that you use a shipping fulfillment company in NJ and ship your products from that state creates what is called a "nexus". When you establish a nexus in a given state and sell to retail customers located in that state you need to collect sales tax, which means you need to obtain New Jersey reseller license (also called Sales Tax ID).
I hope you now have enough material for further research.