They all have similar meanings in your context, but they can't be put in the same position in the sentence. "Also" often occurs in the mid-position (i.e. before the main verb) while "too" and "as well" usually come at the end of the sentence.
He also did work.
He did work too.
He did work as well.
The problem is that all these sentences can mean either of the following:
Other people worked and he also did work / he did work too / he did work as well.
He did other things, but he also did work / he did work too / he did work as well.
In speech, you can stress the word you mean to make the meaning clear. In
writing, highlighting it in some manner like using bold type may
sometimes be necessary to avoid misunderstanding.
(However, if the word "too" refers to the subject of the sentence, it is sometimes placed after the subject: "He, too, did work." In this case there's no ambiguity.)