With a tailbone injury can you do strength training w weights ie squats, leg press, hip abducter and cardio - elliptical?

Varies. It varies somewhat based on the severity of the injury. If it is a fracture, you would be well suited to avoid exercises that put extra strain on that area such as seated military press, etc for 6-8 weeks. If it was more of a soft tissue injury, than basically you would just try to keep your activities to such a level that your pain is not aggravated, but could increase them as tolerated. .