Futurama

Fry is easily the oldest living human depicted in the series, at least if we consider age simply as the difference between that person's date of birth and now. I believe the Professor is stated to be the biologically oldest person in the world at some point, but given that the show itself jokes that he is technically Fry's junior I think in the spirit of things that shouldn't count for much. Various aliens, "god," and other entities may have the technical or biological capability live longer, but only if they're able to survive the end of the universe and continue their existence into the next one... Twice.

I think who gets crowned "oldest" depends heavily on how age is defined in the context of a show where time travel is so frequent. Some additional rambling on that point follows, since I wrote my last comment on my phone in haste and using hazy half-remembered details about a series I haven't watched for years.

Fry was born in August of 1974 and thus at the time of his first freezing at Applied Cryogenics he was 25. When first thawed in the year 3000 he is thus 1025 -- at least chronologically albeit not biologically. Context clues in that season of the show (e.g. ComicCon 3010) indicate that the time machine incident takes place in the year 3010 in the original timeline, thus Fry is 1035 from the perspective of his birthdate when he steps into the machine. I had initially forgotten that the trio make two complete loops of the time span of the universe rather than one, also. Even if the trio did not age for any of that intervening time other than a few minutes here and there while they stopped the machine to search for the reverse time machine technology, they did witness the complete cycles of two universes in super-accelerated form through the windshield and also explicitly can't return to whence they came. So from the perspective of Fry, Bender, and Farnsworth those years have irrevocably passed. Fry, Bender, and Farnsworth now have two entire universe lifespans between the present and their original birthdates, but Fry is already technically the oldest of those three before they even step into the machine.

So from the time of Fry's birth to that moment when they return in the machine and crush their paradox duplicates, two universe lifespans plus 1035 years have passed. (I'll leave calculating exactly how long one universe is to someone else, but the machine shows the end of the current universe to be the year "100000000000000000000000000000000000000000000000000.") Nobody in the show is provably as far dislocated from their original birth/creation date as Fry, so claiming anyone else is would require some assumption or unsourceable claims.

For what it's worth his Lars incarnation is biologically older than him by 19 years by the events at the end of Bender's Big score, having spent an additional 12 years living his life in the past and then freezing and returning to the year 3000 (not 3007 which is when the ending takes place) and living 7 more years in the 3000's timeline before meeting up with the crew during the plot of the movie. He is killed at the end due to being a time paradox clone at the apparent biological age of 59, but prime Fry outlived him by default. Lars died before having two universe lifespans added to his chronological age, also.

In terms of most time actually experienced, Bender is certainly a top contender. Possibly for this reason the Futurama wiki seems to think that he is the oldest character in the show. I think that's pretty debatable, not least because all of the time paradox Benders are indistinguishable from one another. We also can't prove how old the space god is, but he/it is clearly conscious and experiencing events, and has been around for a long time. For completeness, Bender is four years old when Fry meets him (manufactured in 2996) and thus 14 by the time of the time machine incident. But his head was previously buried outside of Roswell for ~1055 years, making his experienced lifetime at least 1069 years by that point. (I don't believe the show specifies what year the crew left from/returned to bookending the events of Roswell That Ends Well. This could be plus another couple of years.) And as said above one of his incarnations -- possibly the prime one, possibly not -- from "way at the end" of Bender's Big Score also went back to the year 2000 to tattoo the time code onto Fry's butt and then apparently took the long way back to 3007 by simply waiting it out in the cave with all the other time paradox Benders. Bender also did the double universe loop with Fry and the Professor, so regardless of what his experienced lifetime is, he's third in the top three for oldest beings since date of birth/construction, regardless. What is less clear is while he traveled backwards in time repeatedly using the time code in Bender's Big Score to steal historical artifacts and returned to the show's present by waiting in the cave, we don't know how many times he did it. Each trip is easily thousands of years, and while at the end all of the Benders explode due to the time paradox effect except one, it's only implied and not outright proven whether the prime Bender is the one who survived (i.e. the one who was ordering the others around and did not take all of the trips himself), whether the Bender who survived and the one who traveled back to 2000 to leave the tattoo are the same Bender, or indeed if the robot we think is Bender is actually Flexo pretending/believing he is Bender since that's also left ambiguous. Either way, Bender's experienced lifetime is clearly the longest of the Planet Express crew and probably anyone native to Earth, although on that point the Nibblonians may even have him beat.

That's because as you have observed the Nibblonians are explicitly immortal in the sense that they do not die of old age, but I don't think when they actually came to be is specified in the show. It's possible but not demonstrated that they could have escaped the natural end of the universe by eating themselves, but where they go afterwards is never explained and whether or not the ones we see in the show are native to this universe or came from a different one is never defined. Any of them we meet could be thousands, millions, or billions of years old but we don't have any specific evidence one way or the other.

TL;DR: Fry has the longest provable time span between his birth and the show's present. Bender has the longest experienced lifetime in the context of us actually having been able to see it. Space god is probably equivalent to the current age of the universe but we're not sure. Some random Nibblonians may have escaped the last universe and now live in ours, being an indeterminate and possibly very old age, but we can't prove that either.