I have three sons,; one is 8 years old and the others who are twins, are 5 are five-years -old twins.

You could also have written it as "one who is…" The original had issues with sentence structure. It also sounds better to combine the two clauses where you describe the twins.

As they are growing up, they always mess with every thing everywhere.

My wife and I follow alwaysalways follow them to clean, but it is very tiring.

Finally we decided to make a family rule that if they don't clean their good[put away?] their belongings, we will hide them away.

Or, "we are deciding," depending on the timeframe.
"Goods" tends to only be used in reference to selling/buying. "Clean" is grammatical, but unless they are getting their things dirty, "put away" makes more sense to me.

Is there any way to teach athem the responsibility tof clean their gooding up after themselves?

This avoids repetition and is also more general than "their belongings."