They all mean roughly the same thing but their position in the sentence is different.
'As well' and 'too' usually go at the end of a sentence.
"I love Japanese food too/as well"
'Also' often goes before the verb
"I also love Japanese food"
It would be wrong to say "I as well love Japanese food", and not very natural to say "I love Japanese food also". It is possible to say "I too love Japanese food" but this would be more common in formal written English.
'Also' is also very common to begin sentences. In this case it is used to give more importance to some new information.
"I love Japanese food. Also, I love Korean food"
Another difference is that 'also' is not usually used in short answers.
If your friend says "I love Japanese food" then you might say "Me too" or "I love it as well". It is more difficult to use 'also' in these short answers. These short replies are useful to master as they are very common in spoken English.
Finally, 'as well' is less common in American English as it is in British English.