Unless you can use flash, which you probably can't, these are situations where a fast lens (anything with an aperture over f2.8 and preferably f1.4) is your friend. A long focus lens with large aperture is your best friend, as then you can crop in camera, get tight in on your subject and eliminate all that awkward lighting.
For lenses that are less than ideal you will need to increase your ISO and accept the higher noise levels.
If you can use a tripod or even a monopod then sharp pictures with slower shutter speeds are possible.
Shoot in Raw so you can adjust colour balance and exposure later. You can steal an extra stop or two by doing this.
Chris