*What do you think would/could happen if the United States were no longer the strongest country in the world?*

I assume you mean in terms of military power?
Or do you mean economic power, or both?

No other country has 12 air carriers battle groups roving the the oceans- and that is a significant aspect of our military power. Another aspect of the US military power is the capability of moving military ground forces, basically anywhere in the world. And in terms of ultimate military power- power we don't really use but has potential last resort, is the capability of nuking any country or the world itself to utter destruction.

All this military might mostly deters other military powers from doing something similar to what Saddam did in regards to Kuwait. Whereas it didn't have much affect upon a situation like where India and Pakistan were facing off with their nuclear weapons- or with their conventional war.

If you simply want the US to get rid of it's nukes, then you probably will encourage other countries to build a significant arsenal of nukes- it's a relatively cheap thing to do. And probably increasing a chance of nuclear war.
If say China or others had our capability or twice or four times our capability of moving ground forces anywhere in the world, I don't see much problem with this. Nor if they had equal or more aircraft carrier battle groups. If some country had such capability, the US would probably work closely with such nations in order to help maintain global security. The US would "use it" and perhaps if dependable lessen our capability to some extent.
Though if you were to simply mothball the US carriers and capablity to move ground forces and only depend on existing carrier groups of other countries to take up any of the slack. Then you would probably see more small wars around the world which would lead evenually to bigger wars.