The LogiCursor can help with moving objects at an angle. Set up the desired angle in Preferences -> Snaps -> Alignment Angles. Zero and 90 are the defaults.

For a 45° angle there is another trick. Right-click on the move reference point. In the popup menu down at the bottom, roll the cursor over the "Construction Lines" option and click on 45 Degree. If you need -45º rotate the construction line using the Gripper.