Recently I started fighting with a group of people every weekend, it's been a few months.

I learned a lot and my pain tolerance and flexibility but more importantly speed increased immensely.

But what I don't get is how to defend when someone taller/heavier kicks you, and I'm not talking about low kicks.. there are quite a few guys, heavy too and they are quick and flexible, Most times they kick me on the shoulders/neck and I parry the block... some times they kicked me in the head, but what hurts the most is kicks to the side of the torso.

Every time they kick, my serratus anterior and lats hurt incredibly for days, this is the third time and the worst one, the last two lasted for 1 or 2 days at most but this one hasn't gone for almost the entire week.

So how and what techniques can one use to better defend the side of the torso area without leaving open new vulnerable spots, specially against kicks?

You're being dumb. Go get training and stop yard fighting. -- JohnP.

STOP … JUST STOP!

There is nothing good down the road you are travelling.

You are going to hurt yourself physically and mentally. You are going to hurt others and not just the one your beat up. You are opening yourself to horrendous legal consequences. Fight Club is a great movie but it is fiction. Living the life of thugs has very negative consequences.

First, go see a doctor about your pains. Hopefully, you did minor damage that will heal with no long term effects. Hopefully…

Second, ditch those friends. They are toxic.

Finally, go and join a martial art class: boxing, MMA, BJJ, whatever… It does not matter. Go train a few times at each clubs around where you live and pick the one you had most fun with: teacher matters more than style. There you (should) get proper tuition in a save environment with professionals looking after you. If you then want to fight in the ring, they will be able to let you do so safely.

I agree with the other answer and commentary; but to directly answer your question, the way you protect your chest is to spar under the tutelage of a qualified instructor, who will no doubt teach you mechanics first, then have you try them on an opponent.

You mentioned blocking, but there is so much to blocking that it's not possible to help you troubleshoot. Your stance, your eyeline, your speed, your power, your aim, your technique, your hips, your hands... all of that contributes to what your opponents are taking advantage of if you do them improperly, and if any one of them is wrong, you end up with where you are at now.

Then you mention fighting taller/heavier, and getting injured for days. Well, in sport fighting, that would suggest you're fighting outside your weight and skill class. Don't do this - there's no advantage for you or for your opponent. Again, a good instructor will help.