Data structure to report all axis aligned bounding boxes intersecting an axis aligned query line
If your query line is x-axis aligned, this is essentially a 2D problem, as you can project all AABBs on the $(y,z)$-plane and answer the following question:
Given $n$ axis aligned rectangles and a query point $p$, report the rectangles containing $p$.

To answer this question you can build a 2D segment tree. This is similar to a 1D segment tree, except that you start building your segment tree according to the projections of your rectangles on one dimension (say $y$) and instead of having some interval $I$ as a leaf, you replace it with a segment tree storing all projections on the $z$-axis of rectangles whose projection on the $y$-axis contain $I$.

You can then query a point by going down the tree and looking for all rectangles which are potential candidates according to their $y$-coordinates and then check among those which "fit" according to their $z$-coordinates.

This leads to $O(n\log^2(n))$ space used, $O(\log^2(n))$ time per query and $O(n\log^2(n))$ construction time.