some students think that listening to English songs will help them in learning the language .为什么that后面listen要加ing呢?难道凡是动词都要加ing吗?那么she said that memorizing the words...怎么said that 后面动词都加了ing呢？还有He thinks studying garmmar is a great way to learn a language 这句话中think后面动词加ing 怎么回事呢？

不是，之所以listen+ing是因为前面think that 的原因，think that后面加动词就要写动词ing

这是动名词作主语.
如果没有-ing,动词listen无法作主语,那么that引导的宾语从句就没了主语,从而使句子无法成立.
你问的另两个句子都是同一种情况,即动名词作主语.
另外,看来你还没有培养起英语语感.让我们分析一下下面这句话：Some students(主语) think(谓语) that listening to English songs will help them in learning the language(宾语从句）.
再来分析一下这个宾语从句：listening to English songs(主语) will help(谓语) them(宾语) in learning the language(介词短语作状语)
顺带一句,所谓从句是相对于主句而言,像上面这句话,Some students think就是主句,listening will help them就是从句；而所谓宾语从句,就是从句充当宾语.