If an online company has a posted policy that says your payment is due on the second of every month, but send you an invoice with terms of net 30 and a due date of the thirtieth, is the invoice date the binding date or does the stated payment policy trump the invoice due date?
This is a direct contradiction rendering the terms ambiguous, and because both terms were drafted by the seller, would probably be construed against them.
is the invoice date the binding date or does the stated payment policy trump the invoice?
It depends on the exact terms of the policy that you agreed upon, which is not clear from your inquiry.
Since this has all been online, I have not signed anything. I did receive an email where he dictates his policy for payment dates.
Beware that having received/read that email is equivalent to having signed the document. In U.S. courts, a party only needs to prove that the adversary was aware of the terms and conditions.
In line with my 2nd comment to your inquiry (about the contra proferentem doctrine) and ohwilleke's answer, you might prevail in a case against that company. Hence the relevance of what jurisdiction you are in, since I am not sure that all countries incorporate that doctrine in their contract law.
As an alternative approach to "having the terms read against the person that wrote them" as suggested by ohwilleke, I put forth another perspective -
The terms of the agreement would need to be known before the agreement was made - anything which comes afterwards (and which does not have the consent of both parties) is irrelevant - thus the terms on the website/stated policy would prevail provided it was clearly laid out and disclosed prior to completion of the purchase.
His saying you "forfeit all previous payments" would appear to be naive on his part, but similarly the payment date specified on the invoice is likely a mistake and I believe would be treated as such.