I guess all requirements in a search domain should be meet (?), so the multiple conditions you use should be connected them with "AND" operator, but they are with "OR" instead (operator is omitted, so default "OR" is used), and so it should always find all "out_invoice"-s for example and even more, united with ones that satisfy any other condition in your domain... it means if customer has already one invoice (or almost any invoice in system may have same effect), then he/she will be unable to make another, he/she will always get a warning "You can not create..." . You'll need to replace OR with AND.

Here is version with  AND  (it should be a bit faster because of nature of "and" operator in Short-Circuit Evaluation, if not considerable fast then at least it's a correct version):

    @api.model
    def create(self, vals):
        today = datetime.now().date()
        inv_ids = self.search(['&', '&', '&', ('partner_id', '=', vals['partner_id']), ('state', '=', 'open'), ('type', '=', 'out_invoice'), ('date_due', '<', today)])
        if inv_ids:
            raise Warning("You can not create invoice for this Customer. This customer already has one or more overdue invoices.")
        return super(account_invoice, self).create(vals)

Please try it. it's interesting if it'll considerable fast then the OR version...