What's the grammar used in "just what quarter he did not now remember" from the book 1984?

Solution 1:

As I think Phil Sweet was trying to indicate in his comment, this is an example of OSV word order:

• O = direct object ("just what quarter")
• S = subject ("he")
• V = verb ("did not now remember") (actually not just a verb but the entire remaining predicate, having already fronted the direct object)

This constitues a main clause that is jammed into the middle of the surrounding sentence. That is perfectly fine, because the parentheses suggest that this is a parenthetical expression, so it does not need to be integrated into the syntax of the rest of the sentence.

(Some people will use different terminology, but I hope that what I've laid out is clear.)

Since you asked for a similar example:

I like green jelly beans (the other types I dislike intensely) and often eat gigantic handfuls of them.

• O = "the other types"
• S = "I"
• V = "dislike intensely"

Solution 2:

Just what quarter he did not now remember.

This is an example of preposing, where it is the complement "just what quarter" (the object of "remember") that is preposed. The non-preposed equivalent would be "He did not now remember just what quarter".

Importantly, a preposed complement serves as a link to the preceding discourse, and must be clearly related to information introduced there. In this case, the complement relates to the earlier mention of "a frowsy little junk-shop in a slummy quarter of the town".