Learn Hardcore Croatian: On više ne radi nedjeljom.

nedjeljom (instrumental, no preposition) means “on Sundays” in a habitual/generic sense.
u nedjelju (accusative with the preposition u) means “on Sunday” referring to one specific Sunday (this coming Sunday, last Sunday, etc.). Examples:
On više ne radi nedjeljom. = He no longer works on Sundays (habitually).
On ne radi u nedjelju. = He isn’t working on Sunday (a specific Sunday).

What case is nedjeljom, and why is there no preposition?

It’s the instrumental singular used adverbially to express regular time. Days of the week commonly do this without a preposition:

ponedjeljkom, utorkom, srijedom, četvrtkom, petkom, subotom, nedjeljom = on Mondays, Tuesdays, Wednesdays, Thursdays, Fridays, Saturdays, Sundays (habitually).

Can I drop On?

Yes. Croatian typically drops subject pronouns when the verb ending makes the subject clear:

Više ne radi nedjeljom. = He/She/It no longer works on Sundays. You keep On to clarify it’s a man, for emphasis, or to contrast with someone else.

Can I change the word order?