The easiest was to gain a substantial amount of strength fast is by doing each exercise till you cannot anymore every other day. An example of doing this can be pushups, do your pushups until you cannot push your body back up, or until your abs cant keep you straight. 

For quick strength have 1 day as lower body exercises and the 2nd day for upper body exercises. Do not use any excuses about how busy you are, you can do all of the following workouts 10 minutes before your shower and bed. 

Upper Body 
  • Pushups on floor 
  • Pushups facing down stairs
  • Pushups facing up stairs
Lower Body 

  • Squats
  • Lunges 
  • Heel ups