我认为正确的是: 

He likes English, as I do. 他喜欢英语，我也喜欢英语（他像我一样，也喜欢英语。）

He likes English the same as I do. 他喜欢英语的程度和我一样。

第一句中as I do是非限制性状语，起补充说明作用，因此用逗号隔开。as I do在书面语还可以为as do I. 还可以改为 and so do I.

第二句为比较喜欢的程度，the same为副词，表示他喜欢英语的程度与我喜欢英语的程度相同。这种状语是限制性状语，不可用逗号隔开。相当于as much as I do. 

我的看法与曹老师的稍有不同，我觉得这四句都是对的，且四句意思相同，后两句加了the same（在此用作副词），起强调作用，也可以换成副词 just, much等。句子有无逗号，只表明说话者在此有无停顿，不影响句子正确性。

同意蒋老师的分析，句子有无逗号，只表明说话者在此有无停顿，不影响句子正确性。又如：

He just wanted the war to end, the same as Wally did.他只不过希望战争结束，和沃利想的一样。《柯林斯高阶英汉双解词典》

likes English as I do.

解析：以上为as引导的非倒装方式状语从句。

结构为：A do sth as B do sth

I'll behave toward them as I would like to be treated.

我会以希望别人对待我的方式来对待他们。

He likes English, as I do.

解析：以上为引导的倒装方式状语从句

结构为：A do sth , as do/did/be +主语(B)

The book was banned in the US, as were two subsequent books. 

这本书在美国遭禁，随后出版的两本也是一样。

He likes English the same as I do.

=He likes English as much as I do.

=He likes English as well as I do.

解析：以上为as关系副词引导程度比较状语，从句作状语（属于限制性）

as代替先行词the same，在从句作状语。

He likes English, the same as I do.

=As well as I do, he likes English 

解析：以上为关系副词引导比较状语从句，在从句作状语（属于非限制性）

as代替先行词the same，在从句作状语。

这四句话，中文意思是基本相同的。He likes English as I do.这句中as是连词，表示方式，英文的原意是他对英语的喜欢和我对英语的喜欢的方式是一样的。如果表示程度，说他和我一样喜欢英语，英语得这样说：He likes English as much as I do. 第二句He likes English, as I do.虽然有逗号，但意思没有改变。这两句有没有逗号，都正确。请看字典例句：Think as I think. Do as I do.When in Rome, do as the Romans do. I taught them to love Valentina as I do.如果as后倒装，那么as就是关系代词了，这时常见的形式有逗号。如she is very gifted, as is her brother.问题中后两句都是关系代词=in the same way as I do. 逗号有无不影响意思。