Share those low-light, no tripod, shooting tips here.
A few to start:
Shoot JPG, rather than RAW. Modern camera built-in noise-reduction is far superior to PC software.
Run test shots to see if you are getting the desired shutter speeds. If not, up the ISO value.
Underexpose by 1/3 to 2/3 of a stop to get faster shutter speeds without upping the ISO value. Just up the exposure on the highlights in post processing if needed.
Lean up against anything you can when shooting. Rest your camera against any surface you can. Even the camera touching a solid surface, pole, or someone's shoulder can help stabilize it. If you have nothing, press the viewfinder up tightly against your eye.
Take a deep breath, shoot two shots when you exhale slowly. Pick the best of the two.
Make sure Image Stabilization is turned on and not in panning mode.