The museum’s open-storage display brings over 500 vintage souvenirs out of attics, desk drawers, shoeboxes, and, museum archives for visitors to view.

Correct sentence - The museum’s open-storage display brings over 500 vintage souvenirs out of attics, desk drawers, shoeboxes, and museum archives for visitors to view.

No comma should ever be used after the word 'and'.

The art gallery features works by contemporary artists from Japan, China, and France, offering patrons the chance to see a kind of passionate innovative art.

Correct sentence - The art gallery features works by contemporary artists from Japan, China, and France, offering patrons the chance to see a kind of passionate, innovative art.

When the order of the adjectives does not matter, a comma should be used to separate them.

Abraham Lincoln and George Washington were two of the most influential figures in, the history of America.

Correct sentence - Abraham Lincoln and George Washington were two of the most influential figures in the history of America.

Do not use a comma before or after a preposition.