I dont know what happened to my sketchup model but i used to be able to move objects and edges in a straight line, whether it be the red, green, or blue axis, without using the arrow keys to lock the object to a specific axis. But now now i cant do it anymore. When moving objects or edges from a top parallel projection view they dont auto lock to an axis.
I tried creating a new file and the inherent axis constraint works but for my old file it does not. I’m pretty sure its a setting of some sort that i toggled off but i cant seem to be able to figure out.
I stripped down the file and left a square from the top view to manipulate. As you will see there is no way of moving the edge or the entire square in a straight line. Its supposed to automatically lock to any axis and then release if you deviate it too much, all without using the arrow keys to lock it to any specific axis. I dont know why its doing that. The auto locking only works if i move the object up or down along the blue axis but not along the red or green axes.
I find no issues with moving things in your model, I tried it in both Web and Pro.
I note that the axis has been moved, that may be significant and perhaps resetting it will solve the issues on your end.
I would also turn off length snapping, it tends to cause errors.
All directions seem to be working as should: constrained to line when locked either by [Shift] or by [Arrow] keys. (some cursor info show as being “Constrained on line” some show as “On Red/Blue/Green axis”).
So nothing wrong on this end. Only the moved axes as @Box already mentioned.