Bodyweight exercises would be your best bet.

Variations of lunges, squats, push ups, dips, jumps, burpees etc.

These would all give you some form of resistance without using weights.

Regards,
Dev Chengkalath
www.devchengkalath.com

Jugging, help you strength and give you more stamina

Not just weightraining but also cardio vascular endurance training,proper nutrition,yoga for physical&mental, strength+circuit training&proper sleep. Because strength means physical/ mental power&endurance.

My 2 cents....
I would start training using slow movements that stretch the muscles and more importantly stretch and strengthen the tendons. If big muscles are not a concern but strength is, then you do not need heavy weights. Although weights might get you there more quickly.
Use items in the home like a pan full of water, or books in a pillow case, etc. There are many ways to add weight to an exercise using everyday items in your house.
Use slow movements and many, many repetitions, this will give you strength and endurance.
But concentrate on strengthening the tendons, this provides lasting strength that support the muscles.

There are so many ways, dance, pilates ,martial arts to name but a few.

The harder question is what do you want to achieve, when you have decided that then the exercise style is much easier to find.

Body weight exercises will help.I must ask though why you do not want to train with weights?Is it because you can't to the gym or what?If you want the best results buy some dumbells at the least.

Plyometric exercises are good to exercise at home, I've always used them, and managed to increase my vertical leap significantly.