Warning - this page will have a lot of spoilers.

Before Aru Shah and the End of Time

2005

On the day of Aru's birth (Feb 15 2005), Krithika imprisoned the Sleeper in the Diya of Bharata.

2015

Aru Shah and the End of Time

2017

On the first day of autumn vacation for the students of Augustus Day in Georgia, Aru Shah wishes for something cool to happen, bothers her mom, and is confronted by Poppy, Arielle, and Burton (three of her classmates) on her lies. Aru says she'll light the Diya of Bharata to prove what she said about it was true (that it had a demon in it). She takes them to the diya, types in the password to turn off the safety precautions (her birth-date)and plans to act possessed as soon as she lights the lamp. Poppy stole her brother's lighter, and Aru uses it to light the diya. The Sleeper is released, and Poppy, Arielle, Burton and Krithika are all frozen. Boo arrives via elephant, and Aru begins her quest.
Also on day 1, Aru meets Mini, talks to the makara on their way to the Council of Guardians, gets claimed, comforts Mini about her status of Daughter of Death, and is given countdown henna by Urvashi, who instructs the trio of Aru, Mini and Boo to find the three keys to make their way into the Land of the Dead and see what they need to in the Pool of the Past.
Though the quest lasts ten days, the story has a time skip at the end which brings the story to an end at the beginning of winter break.

Aru Shah and the Song of Death

2017/2018

Picking up less than 24 hours from where Aru Shah and the End of Time left off, at winter break, Aru and Mini are hiding from zombies and trying to find their newest Pandava sister (Brynne). They manage to catch up to her after a brutal fight with a rakshasi shapeshifted into the form of Aru, but the encounter turns hostile once Brynne wakes up and attacks Aru. The two girls, along with Mini, are separated from each other, though, and taken to their own respective cloud bubbles over the Council of Guardians. After a few minutes, they're summoned down to face the Council, including Uloopi and Takshaka. It's explained that they are to undertake a quest to prove their innocence from the theft of Kamadeva's bow and arrow, and that they have ten days for that before they're sentenced to lose their memories of the Otherworld.
This story ends on the date of February 15, which means that although Aru started the story at 12, she ends at 13.

Aru Shah and the Tree of Wishes

2019

This story begins on March 15, 5 days from Holi 2019. Aru, Brynne, Mini and Aiden rescue Nikita and Sheela from the Sleeper, the prophecy comes out for both the Sleeper to know and the devas, and after a disastrous session with Opal and the discovery that Kalpavriksha was a fake, Aru realizes the prophecy must be about finding the real Kalpavriksha and wishing on it.
This story ends on March 20, the first day of Holi.

Ages

Aru

Aru is twelve as of Aru Shah and the End of Time, twelve-thirteen as of Song of Death, and newly fourteen as of Tree of Wishes.
Her birthday is February 15, meaning that if Aru Shah and the End of Time began in autumn 2017, her birth year would be 2005. The reasoning for Aru Shah and the End of Time beginning in autumn 2017 has to do with...

Mini

Mini is around Aru's age in Aru Shah and the End of Time, meaning she was probably eleven, twelve or thirteen.
Mini was confirmed by Roshani Chokshi as having February 29 as her birthday, meaning she was born on a leap year. The leap year closest to Aru's birth year, which HAS to be at least around 2005, is 2004. Therefore, it makes sense for Mini to be born in 2004, and Aru to be born a few weeks less than a year after.
This means Mini was 13 as of End of Time and Song of Death, and recently 15 as of Tree of Wishes.
If you're counting by leap years, End of Time and Song of Death Mini was 4 1/4, nearing 4 2/4 by the end of Song of Death, and Tree of Wishes Mini was 4 3/4.

Brynne

Brynne's birthday was confirmed by Roshani Chokshi to be May 8.
This could mean she was born May 8 2004 or May 8 2005, although it's likely she was born May 9 2004 since it's plausible she and Aiden were in the same grade level at Otherworld School.
Brynne would be either 13 (younger than Mini) or 12 (younger than Aru and Mini) in End of Time and Song of Death, and 13 or 14 in Tree of Wishes.

Aiden

Speaking of Aiden, he's two grades above Aru Shah, a seventh grader, in End of Time and Song of Death, meaning he's 14-15 years old if he hasn't skipped any grades.
If he was born in late 2003, his age would be close to Brynne's, so that's the more common assumption.
Aiden was therefore 14-15 years old for End of Time and Song of Death, and 15-16 years old for Tree of Wishes — it makes the most sense to go with the lower options.

Nikita and Sheela

As they're twins, it's safe to say they share their birthday.
Nikita and Sheela are 10 in Aru Shah and the Tree of Wishes, which is logically early 2019, meaning that they would have been born in either 2008 or 2009.

Rudy

Rudy has no canonical age, but he's likely in between the youngest of the Potatoes (Aru, at 14) and the oldest (Aiden, at 15 or 16).

Timeline / Aru Shah and the End of Time