I am happy.=我开心=我快乐。But pure Chinese we also translate it into“我很开心（快乐）” I am very happy.=我很开心（快乐）=我非常开心（快乐）。"很" is a adverb,it is usually connected to a adjective.It just shows a degree.

we rarely say :我乐 or 我很乐 。 when you feel happy , you can say : 1 我很开心 我真开心 我好开心 (I am very happy ) 2 我很高兴 我真高兴 我好高兴 (I am very happy)

Both ( 我乐！) and (我很乐！) are incorrect. I suggest that you translate HAPPY into 快乐or开心 instead of 乐, then you would not have problem with the translation. Generally, when we use Chinese to say 'I'm happy' , even there is not 'very' in the sentence, we still would say 我很快乐. It sounds more oral and natural. SO, both of 'I'm happy' and 'I am so happy' suggested should be translated with the word '很' . If you want to emphasise on the 'Very', normally, it still says as 我很快乐or 我很开心, but the tone would be more excited . or you can put a Chinese modal word '啊' after the sentence. i.e.我很快乐啊！我很开心啊！我好快乐啊！我真的很开心啊！我非常的开心啊! 我快乐极了！我快乐的不行了！ Hope it helps~

我 快乐

the first is 我快乐,the second is 我很快乐