If following strict a Riegelbau framing modalities, or other historic formats, then each region (as David has suggested) has its individual predilections. If being fully historically accurate, then one could follow the given regional modality as a guide.
It seems mostly important that they be balanced/braced against each other on each face of the building, but are there any off-axis loading considerations I should be careful of?
Yes..."compression resistance" in "oblique bracing" works better in a balanced format. Further, "Oblique Bracing" tends to "work" more effectively when larger in size of the triangle it forms, there by not acting as a fulcrum against the corresponding joinery. Also, "oblique bracing" modalities also function better in the "buttressing context" (i.e. at the base of a post) and can also work very well in the "horizontal" configuration within floor and roof systems as well. (i.e. "strong back" and "dragon beam" systems)
If this structures is not an example of historic replication, then "bracing" can take on many different formats that may be not only applicable but more easy to facilitate.
"Bracing" does not have to be "oblique" in nature to be functional and/or enduring. I seldom use "oblique bracing" systems in structures I design or facilitate. Asian (and some European) modalities also rely heavily on "horizontal bracing systems" and/or "infill systems" to give the structure the requisite "resistance" against racking that it needs to be enduring...Horizontal systems typically are less difficult to facilitate/build. Additionally, horizontal systems of bracing tend to never interfere with fenestrations, ingress/egress logistics within the frame and other consideration that oblique bracing can often obstruct and incomber.
