He said he should go

是不加to的,should 后面直接跟动词原形.
动词是有两个,只要分清句子的结构就行了,
said 后面的he should go 充当的是宾语从句,也就是说,它作整个句子的宾语,关于这类问题,只要分清它的结构就不难了.

He said he should go是对的, should后要求跟动词原形.

He said he should go

go

He said he should go,should(情态动词)后要求跟动词原形.

肯定不能用to go.
如果要写的标准，再加个that.
He said that he should go.