I'd say "I have a strong willingness to learn".

I wouldn't use 'willingness'. In conversation I'd say 'I'm really keen to learn' or 'I really want to learn' :)

A strong willingness to learn.

"Big willingness" and "hard willingness" sound comical and even childish. I guess "strong willingness" is a collocation you have to learn... like many others.

"Willingness" is not used so much in conversation, as the previous comments have stated. From what I can tell, you are trying to increase the sophisticated nature of your writing, which is a great idea! I'll write some sentences below that mean similar things to what you are saying: I have a strong desire and passion to learn more. (Common wording for what you are saying) I have immense alacrity to learn more. (Alacrity is not a word that the majority of people know. Only use this is more academic environments. You could also replace alacrity for "fervor.") My suggestion: "I have a strong desire to learn more." This is the most common and understood.