I did some digging and found that Natsu, or atleast the Natsu we know, is around 20 years old but I want to know his birthday which I can not yet find an answer for.
I believe that Natsu is a year older than Lucy. The year they came from was 377 to be exact, if you then add the year 777 it's exactly four hundred years so Natsu would have been 11 years old as Lucy was 10. So if Lucy was born 767 that means Natsu was born 366, as to the exact day it's unknown but because his parents named him "Natsu" (summer), as the first day of summer is around the middle of June and not July we could say Natsu's birthday is June 20th 366. http://fairytail.wikia.com/wiki/Lucy_Heartfilia
↑ Fairy Tail Manga: Chapter 465, Pages 11-13 ↑ Fairy Tail Manga: Chapter 468, Pages 2-14 ↑ Fairy Tail Manga: Chapter 468, Pages 14-18 ↑ Fairy Tail Manga: Chapter 400, Pages 15-19 ↑ Fairy Tail Manga: Chapter 414, Pages 8-17
His birthday is July 7th concluding to Hiro Mashima. The year has not been specifically been said yet, but it is some time in when dragons disappeared. Since Natsu was trained by Igneel, he must have been born before this date, presumably several years before to allow time for training and such. So around X777.