The numbers are for the annual New Year's lottery. When you send someone a card, you've also entered them in the lottery! (Kind of like giving Scratcher tickets at Christmas.)
Although there are a few big prizes, most of the lucky winners will receive the souvenir sheet issued for that year's new year's stamps. (This is footnoted in Scott under the stamps. -- I've thought about putting together a webpage that shows them.)
Here are a couple of posts from people who've won the souvenir sheets in recent years:
By the way, your third example shown, with the big "T" crossed out, is an interesting little item. I'm pretty sure of this, but am willing to be corrected, that this shows that the card was originally charged postage due, I'm guessing for the international postcard rate to the US.
Judging from the other used examples, it looks like mail sent from Japan to APO addresses in Japan should be charged just the domestic rate (even though it has that US-style zipcode on it), and that the postage-due card originally was flagged but ended up being cancelled. (Or else paid -- that might be a possibility as well.)
You definitely did well at that club auction! Congratulations!
Wow! How interesting! I appreciate all of the information - I doubt that I would have been able to gather all of that information. These examples (the cards and covers) were part of around 55 covers. Most are posted from Japan to Camp Drake which is in Japan. Many of the covers are run of the mill, so to speak, but there are several more that I will add to the cover topic I created earelier. Thanks so much for the education! Don