If the expiration is a certainty, then "will" (rather than the subjunctive "would") can be correct:
Your offer will expire by 31-Oct-2018.
Your offer will expire on 31-Oct-2018.
("Expire by" implies some uncertainty in the date that the offer will expire-- it could be sooner than 31 October.)
It is also acceptable to use the simple present, as you suggest:
Your offer expires on 31-Oct-2018.
This is the best wording -- simple is often best.
It's difficult to construct a scenario where "would expire" is correct, because it implies uncertainty that the expiration will happen. Even these uncertain scenarios are better with "will" rather than would:
We have sent your bid to Alice. If Alice fails to respond, your offer will expire on 31-October-2018.
Some states have time limits on gift cards. If this applies to you, your offer will expire on 31-October-2018.
The scenario has to be very uncertain for "would" to make sense:
Alice sent a letter to Bob. If Alice's letter is delayed more than a week, your offer would expire before Bob receives the letter.