Firstly, it is a word. Secondly it is perfectly acceptable. Thirdly, if you've got more than two points and you've already used 'firstly' and 'secondly' you should use 'thirdly', and 'fourthly' and 'fifthly' if you need them. Don't be afraid to make your speech stand out and get noticed. Okay?
According to my research, thirdly is a word, simply indicating that it is next after second. If one has already said firstly and secondly, then to use thirdly is fine.
I really think "firstly" and "thirdly" sounds strange. Don't use it! Of course, "secondly" is perfectly fine when speaking. This means you would use "first of all", "secondly", and "finally" when making a bullet point speech.
