You can build quite an extraordinary level of strength with nothing but your own bodyweight; don't believe anyone who tells you otherwise. High reps to failure are in order for endurance, low reps of progressively more difficult variations for strength.
Pull up variations (can be done hanging from a doorframe by your fingertips if needs be) : Regular pull-ups, pull-ups from L-hang position, one-arm pull-ups
Pressing movements: Regular push-ups, push-ups with feet elevated, handstand push-ups (either free balancing or with feet on a wall for balance), plyometric push-ups, fingertip push-ups, one-arm push-ups, one-arm, one-leg push-ups, one-arm handstand push ups (!)
Core: Manna progressions (L-sit > V-sit > Manna), Planche progressions (from tuck planche), dragon flag, janda sit-ups, regular sit-ups, isometric tension, any kind of gymnastic hold requiring you to hold your body straight.
Squat variations: Bodyweight squat, one-legged squat, one-legged jumping squat for height or distance or both, one-legged squat with pauses along the way, all kinds of jumping.
Also, as this thread is about low-budget training, not bodyweight only training, I advise you to consider building yourself a sandbag (see here
). You can also make yourself a wheel for ab rollouts from the wheel of an old pram or shopping trolley. A homemade skipping rope will serve you well, as Cord suggested. Use your imagination!