Quote Originally Posted by Uchiha Barles
The Naruto story has one very enduring constant: strength trumps all. It trumps experience, it trumps inventiveness, cleverness, it trumps numbers, everything. If there's a significant strength difference between opponents, the weaker opponent certainly cannot beat the stronger, but he also cannot hide from the stronger, cannot run from the stronger, cannot outsmart the stronger to any significant effect. The only time variables other than strength matter, is when the opponents are evenly matched in strength. There used to be this rock/paper/scissors theory going around about which fighter would be able to defeat which other fighter, but clearly that's been done away by a preponderance of evidence against that theory found in the manga. Strength far outweighs all else.
I can definitely see why this might seem like the case, but I think it's only this way because it is so easy to overlook cases where this doesn't hold true. Naruto's whole Rasengan technique is not pure strength. It's a technique. It required inventiveness and cleverness on Naruto's part to learn. Power in the manga is either raw power, lots of chakra, or bloodline limits/innate talent. You can't say learned techniques are power; otherwise, you negate the fact you need inventiveness, cleverness, and experience to develop these techniques. You would in effect be saying that power, which includes experience, cleverness, etc.., always trumps experience, cleverness, etc...

Deidara (spl?) had much more raw power than Sasuke. He also had much more experience... He even was able to counter Sasuke sharingan. How did Sasuke win?

Turning it around, Gaara had much more raw power than Deidara.

What about the puppet guy? Was Sakura + Old lady much more powerful?

Sage-mode Jiraiya was a lot more powerful than Pain, but Pain had the upper hand as far as technique/inventiveness.

Going way back, was Sasuke really stronger than Kyuubi Naruto when Sasuke beat him?

There are many examples where the stronger person loses.

As far as a weaker opponent cannot run from stronger opponents, explain the very first Arc where Zabuza ran. Naruto escaped the first encounter with Itachi, Itachi got away from Jiraiya. The genins got away from the chakra prison in the Sasuke chase arc.

Yes. You do have a case with many examples, but if you look, you'll also find many counterexamples.