I understand that many JR stations have luggage offices (手荷物預かり所) that will temporarily keep your luggage for a fee. Is it possible to leave luggage there overnight?
Yes, most luggage counters will hold your bags overnight or longer, eg. the one in Tokyo Station can hold them for up to 15 days. 410 yen/day for the first five days, 820 yen/day from the 6th day onward. Ask for the "Rail-Go Service" (レール・ゴー・サービス); the weird name is because you can also send bags to/from here via package delivery services like Takkyubin.
Link in Japanese: http://www.tokyoinfo.com/guide/faq/index.html#q4-2
You can put it in the locker. the price is charged per day based on this article, but your locker will be emptied after three days. You can leave your luggage overnight.
The cost of coin lockers is based on calendar days (midnight to midnight) and is typically 300 Yen for small lockers, 400 Yen for medium lockers and 500 Yen for large lockers per calendar day. In other words, if you use a small locker overnight, you will have to pay an additional 300 Yen when picking up your luggage the next day. Lockers are emptied by station staff after three days.