What is the ruling on swearing by "and by God, in your hand" in this situation?

If you intended in your heart, when swearing an oath not to drink tea, that this oath should be binding, then it is a binding oath. If you drink tea, you will have broken your oath and expiation will be incumbent upon you. However, if you did not intend that, and it was merely a customary utterance that flows from people's tongues, then it is a 'laghw' (unintentional) oath, and nothing is incumbent upon you for it.