Bones look weird after importing UE4 Standard Mannequin

This is because of the Maya rig having bone orientations that are not allowed in Blender. If you check Automatic Bone Orientation on import it will look better, but it will then not export to UE4 the right way because you changed all of the bone orientations so it’s no longer compatible with the UE4 skeleton.

I don’t really recommend using the UE4 mannequin rig that way at all, instead you could use an addon like UE4Tools (http://www.lluisgarcia.es/ue-tools-addon/) that has a control rig and the orientations set up to be reasonable within Blender. It’s still not compatible with the UE4 mannequin skeleton but you can either retarget your animations to the UE4 mannequin (will be 100% accurate) or just use the UE4Tools as your rig instead and retarget UE4 animations to your new UE4Tools skeleton.