100 Yen Banknotes From 1953

Can anyone tell me whether these are still legal tender? Thanks.

They should be. But you may find rejection in attempting to use them for shopping.

I would go to a bank and exchange them.

They're legal, but I would go to a coin shop where they would buy it for about 5000 yen a piece if it's in good condition.
http://xn--nckg3oobb6964c1ca565hk28g8pm.net/kaitori/kosen/322

Still "legal", but actually cannot use for payments, shoppings, eatings, and no accept any vending machines.
http://www.boj.or.jp/en/note_tfjgs/note/valid/index.htm/
(no mentioned about old notes, read below FAQ with Google translate.)
http://www.boj.or.jp/announcements/education/oshiete/money/c07.htm/

BC most store/shop staff(mainly under 35) don't know legal or not and even existence of such old notes.
(also recent years foreign workers a lot mainly convenience stores.)
Also vending machines have not such old note identification as function.
But all vending machines have usable money signs as "caution" of notes/bills.
This is regular ones of train tickets.
https://www.1101.com/tonomariko/images/164_IMG_3463.jpg
https://i.ytimg.com/vi/-YI8XtdeH5U/maxresdefault.jpg
This is regular one of drinks, only 1000Y note.
http://www.geocities.jp/otearai/senen3.jpg
This is ramen shop's ticket one.
http://www.n-nagi.com/wp/wp-content/uploads/2015/06/FullSizeRender46.j...
http://livedoor.blogimg.jp/amaozisan/imgs/2/6/2634da9e.jpg

If those are super clean(like new) or error ones, it may be high by money collectors.
If not so and just have a lot, you should exchange at major big bank in Japan. (not "of" Japan)
One should be left as a small mine or a memory of Japan.

Still "legal", but actually cannot use for payments, shoppings, eatings, and no accept any vending machines.

Vending machines may not accept them, but according to the 2nd link that Thonburi provided, it clearly says (below) that the notes can be used for payments typically including shoppings and eatings.

なお、一度発行された銀行券は、法令に基づく特別な措置がとられない限り、通用力を失うことはありません。

Of couse, you might have a problem with shop/restaurant clerks who do not know the note, but still you are legally allowed to use them. In any case, the easiest way to use them is to go to a bank and have them exchanged.