he was afraid that someone else would take away his clothes

1 that引导一个宾语从句，这里的that可以省略，直接：
he was afraid someone else would take away his clothes

2 else别的人，else表示“其他的”，比如someone else的意思是 其他的一些人

3 一般would的语气比较轻微，比较礼貌些，而在一些语境中又含有猜测、可能的意思，也用来表明自己的某种意愿

句型就是that引导了一个宾语从句。

he was afraid that someone else would take away his clothes.
是两个句子
- He was afraid.
- Someone else would take away his clothes.
That 把这两句子连起来。

不过that在这里可有可无，这样也可以的：
he was afraid someone else would take away his clothes

else 强调 someone

would 是 will 的过去式， 在这里和轻微语气没什么关系。

that引导的是一个同位语从句,后面那个would是过去将来时态，因为他前面用的是was

he was afraid that表语 someone else其他 would take away his clothes虚拟语气.

that引导的是一个同位语从句,而would是will的过去时.相信我,没错的!