Now I looked over Imperial Library's Timeline but I can't manage to put together what exact dates the various games take place in. Could anyone help?

From 3E 389 to 399 is Arena
3E 405 to 417 is Daggerfall
3E 427 to 432 is Morrowind
3E 433 to 4E 1(?) is Oblivion

Arena is over a span of 10 years, Daggerfall is over a span of 12 years, Morrowind is over a span of 5 years, and there's not much for OB at the current moment, other than what I surmise to be...~3 years, give or take a year. The time between Arena and DF is a 6 year period, DF to MW is 10 years, and MW to OB is a year. The total universe time we as players have played comes out to be ~46 years total.

So for those who wanted to continue a character from Arena to OB, the person is likely to be 64ish by the time OB is over, assuming you are a human and started out at 18 in Arena. Orc characters are going to have a harder time justifying their characters from A - OB, due to the really short life-span of 40ish years orcs have. Elves live a long time, so the whole getting older part is more minimized, and largely unnoticeable if you've been an altmer mage, or a dunmer mage