If my wallet (private key) is stored on a small USB stick, can I purchase anything using bitcoin if there is no power/network near me?
By this, I’m assuming you mean you have no connection to the network. There is infrastructure built to relay transactions through SMS and satellite services, but let’s pretend you don’t have access to those either.
In that case, you could trade your USB stick for whatever goods/services you’re trying to purchase, but your counterparty will be taking on significant risks:
If there is no way to connect to the network and check the balance on the address you claim to have the private key for, the counterparty will have to believe that the appropriate amount of funds are indeed held at your address
Your counterparty will have to trust that you do not have a backup of your private keys, otherwise you could make the trade, and then use the backup of your keys to spend the coins back to yourself, before the counterparty can sweep the address.
You may be interested to look up OpenDime, it is a product that allows you to give someone a private key that is provably not backed up.