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, I have added 30, 45, and 60 since I use them often. Just enter your angle/s followed by a semicolon. The last angle entered will not need the semicolon after it. Don't include the degree symbol, TC will add that for you after you close the dialog box. Now when you move an object the LogiCursor will popup to assist your move.
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.