What is the correct word order for words 跑步 and 轻快?
I see no issue with 轻快的跑步 when you consider 跑步 (as a whole) a noun word. 

If you take 跑步 as a verb, then 轻快地跑步 is ok. 

For example, 


  轻快的跑步能让我们的身心得以放松。 // used as a noun.
  
  我们在操场上轻快地跑步。 // used as a verb


In fact, I'd rather say 跑步 is used as a noun more often than a verb. For example, 跑步是一项很好的运动. 

The single character 跑 is often used when serves as a verb, instead of 跑步. For example, 他跑得很快。We wouldn't say 他跑步得很快. This is because we take 跑步 as a noun usually. 

So, 轻快的跑步 does make some sense in some circumstances. 

跑步轻快 is a possible usage too, because 跑步轻快 could be considered to be the short version of 跑步跑得轻快. 

However, 跑步的轻快 is not valid in any case, because 轻快 is adj or adv. You could say 跑步跑得轻快， but 跑步得轻快 is wrong because (as mentioned above) 跑步 is often used as a noun word.