Answer 1: over 80 (doesnt say)
So as the other Dragon Slayers mentioned in Fairy Tail, except Laxus Dreyar ( 2nd Generation), who is 23 years old.
Answer 2: We were never told and over 80 isn't necessarily true. He himself isn't over 80, his Magic is considered to be over eighty year because it's classified as ancient.
Answer 3: The reason Answerer 1 said over 80 was because he couldn't leave Freed's runes, but Gajeel couldn't either so that's not necessarily true. So, as Answerer 2 stated Natsu's age is currently unknown.
Answer 4: If your refuring to the episode of Laxus trying to take over the guild, Natsu and Gajeel couldnt escape the runes because they used Dragon slayer Magic, not because they were over 80 years old, even though the manga and anime dont say, my guess is that Natsu would be around 17 to 18 years old. but its only a guess not a fact.
Answer 5 :To be honest Natsu's true age haven't been revealed yet,want to clear something that non of the previous answers have touched, the fact that Zeref who is pretty ancient know Natsu,don't know about Gajeel's condition but you might consider the fact that Natsu might be over 80,possibilities considered here.
Answer 6: To sum it up : Natsu's age is UNKNOWN and was never revealed.
Answer 7 : I would think around 17-18 because in the anime you can see that he grew older at the pace Gray, Cana, Erza, and others grew at so if he was 80 that mean 6 years ago he looked as young as Gray but 74?
Also the reason Zeref knows Natsu is because Zeref had been watching Natsu and that's why Natsu doesn't know Zeref. From what Zeref said I'm guessing Zeref was waiting for someone strong enough to finally killl him and he that's why he was watching Natsu and knew who he was.
Answer 8 : Actually Answerer 2 was right, the reason Natsu nor Gajeel can't get out of Freed's runes is not because they're as old as the master, but because their Magic is old, so Natsu's age remains unknown. Next is Answerer 7's answer. The reason why Zeref knows Natsu, is not because he has been watching him, although that is also correct but, maybe (and this is just a theory) because there have been a prophecy that Natsu is the one that wil defeat acnologia or something. I said this because in the chapter "All Feelings Unite" the old man said that the Grand Magic Games was also called "Ryuuousai". And if you would look clearly, you would see that the man fighting the Dragon in the picture is wearing a scarf, so if that's the case then the pictue might be a prophecy of some sort, and the man is Natsu, defeating acnologia.
Answer 9 : Natsu is 15-18 (Cana being slightly older than Natsu is shown consuming alcohol, keeping in mind the laws, she can't be shown consuming alcohol unless above 18, also keeping in mind Natsu's height after the birth of Happy and the period of disappearance of Lisanna, he fills the category). The reason both Gajeel and Natsu couldn't get out of Freed's runes is because all the Dragon Slayer's who lost their Dragons on the 7th, actually didn't lose their Dragon's but more like their respective Dragon's got inside their bodies somehow. Dragons obviously ageing more than 80 years, fulfilled the condition of Freed's rune, disabling either of the Dragon Slayer to leave the building.
Answer 10 : Same as Lucy i think . According to the answer 8 im agreed with it (if you would look clearly, you would see that the man fighting the Dragon in the picture is wearing a scarf) i think the Dragon is Acnologia because the complexion on the Dragon body. I bet the scarf that the man wearing is same with Natsu scarf (because the scarf is scales patterned). I think the man close with Igneel (my opinion) and he is using Igneel fire Dragon Slayer Magic and he is Natsu real father !
Answers 11 : From his appereance, its about 17-20. and now there's Eclipse's wich allow people go trough time. Like here, maybe? -> Natsu comeback to past and meet Zeref. He told him he's future, and somewhat Zeref want Natsu to kill him. and when he comeback to the future. IT'S CHAOS! Answer 8 is more logical.
Answer 12 : Physically, Natsu appears to be about 17-18 being on par with Gray or Lucy. I think that (Partially going along with Answer 8 and Answer 10) Natsu could've gone back in time using the Eclipse to face Acnologia. As can be seen the person facing the Dragon in the picture is most likely using Fire Dragon Slayer Magic, like Natsu uses. So the person in the pictue could've been Natsu himself, but him somehow not having any recollection of what had happened.
Answer 13 : Physical age 17-18 actual age 24-25 (due to 7 years gap). The person in that painting is actually Acnologia as it is written in the manga He was once a Dragon slayer. After slaying 1000's of Dragons and being drenched in their blood he started to take on the form of a Dragon and called himself the King of Dragons, And with the help of Zeref was turned into the modern day Acnologia. The Grand Magic games are actually a celebration of him killing a thousand Dragons hence "The festival of the Dragon King"
Answer 14: Natsu is more old than anyone in Fairytail Guild just like Gajeel Its not that there Magic was ancient but they are ancient because how could they have met their Dragons in the same time. It was well said in Fairytail that Dragons do not exist in their time also we see that when the eclispe gate was opened Dragons came from the past so there is no way Natsu could have met his Dragon in the present. So it means Natsu and all the other Dragon Slayers are very old. Also their is a theory that the reason zeref knows Natsu is that they may have met in the past.
Answer 15: FOR OFFICIAL SAKE: Only Hiro Mashima knows.