Hi flower , "Anyway " means in all cases , whatever happens , anyway so and so ---means in all cases ,regardless from the statement before "anyway" the statement that comes after is a fact , will be or should be . He forgot to call her .Anyway she doesn't care anymore. So it means whether he call or not in all cases and under any circumstance she doesn't care . "by the way" is used when someone suddenly remembers he/she wants to say something most probably related to what is being discussed at the moment . It is like hinting or making a notice about something related to the subject or person in a discussion. I know you like him , by the way he likes you too. She will arrive tonight from Paris , by the way she is a very nice girl .

anyways can b usd to describe a situation in which u can't change the situation----like " this time u hvn't got good marks....anyways! work hard the next time" it can also b usd like "u wud get a punishment anway so its better not to lie" by the way is an informal word which is usually usd to change a topic --- for eg "by the way whats ur name"

just when you ask about anything