For your second sentence it would be more natural to say:

 'I was finished with job last month as it was temporary job.'

->

'I finished with my job last month as it was a temporary job.'

I have finished ~ / I was finished ~

When I was talking to my friend, she said 'what are you doing these days?
so I said 'I was finished with my English course last month.'
Is this sentence correct?, or 'I was finished with job last month as it was temporary job.' How about this sentence?

What's the difference 'I was finished with my English course last month.' and 'I HAVE finished with my English course last month.' ?

ANSWER:

If you say, "I was finished", it you are emphasizing that the action already happened. But since you are answering your friend's question, "what are you doing these days", it is more natural to say "I finished my English course last month".