Mahabharata (Hindu epic): What would have been the age of pandavas and other characters at the time of the kurukshetra battle?

Short answer

Yudhishthir - 91 years; Bheem - 90 years; Arjun - 89 years; Nakul & Sahdev - 88 years.

Long, a bit less relevant, but certainly interesting.

Following is the timeline copy-edited-pasted. More details about events, war statistics (highly exaggerated they seem though, killing billions of people), names of years and months can be found on the source of this information - The Mahabharat Chronology. The number in (parenthesis) is the time in years from Yudhishthir's birth.

[-16] Karna's Birth.
[0] Yudhisthira was born. That was just [127-5-25] prior to Kaliyug [roughly 3229-8-15 B.C]
[1] Bhima's Birth
[2] Arjun's Birth [Phalguna Full Moon Day]. Lord Krishna's birth [Shravana Dark 8th day] who was 6 months older to Arjun.
[3] Nakula's and Sahadev's Birth
[1] Duryodhana's Birth : Just one day after Bhima's birth. From that day onwards everyday the rest 99 Kauravas and their sister were born.
[16] Pandu died 
[29] Pandavas were brought to and stayed in Hastinapur for 13 years. They learnt archery under Drona.
[31] King Drupada was taken captive. Yudhishthira was made Crown-Prince.
[36] Pandavas stayed at Hastinapur for yrs. 5-4-20
[37] The Lac Palace was set on fire.
[38] Demon Hidimba was slain. Ghatotkacha was born and he grew up as an adult immediately.
[39] Demon Baka was slain. Princess Draupadi's Swayamvaram took place.
[40] In Panchala Kingdom, Pandavas stayed there for yr. 1-0-15 days
[45] Pandavas were received in Hastinapur. They stayed in Hastinapur for 5 years and 6 months. Indraprastha City was being built during this period.
[46] Yudhisthira was coronated.
[58] Arjuna went on pilgrimage for 12 years. He married Subhadra, and Abhimanyu was born. The Khandava Forest was burnt down. Mayasabha took yrs. 1-2-0 days for construction.
[60] Pandavas entered Mayasabha
[76] Rule in Indraprastha for 16 years. Wrestling started between Bhima and Jarasandh continued for 14 days, and Jarasandh was killed on 14th evening. The Rajasooya Yadnya began. The two dice-plays were played in an interval of 4 days.

So Pandavas ruled for a period of yrs. 36-6-20 days 

[76] Forest Life : Forest life started. 12 years forest exile and 1 year anonymity 
[89] Pandavas declared their identity
[91] Shri Krishna's Peace talks
[91] The Great Mahabharat War started, Lord Krishna's famous Bhagavad Geeta discourse with Arjuna. Yudhishthira was crowned again.
[92] Ashwamedha Yadnya began.
[127] Yudhishthir ruled for yrs. 36-2-15 days. Kaliyug started and Krishna finished hisAvatar. [B.C 3102-2-20 at 2-27-30 P.M]. Seven days later, Dwarka city was submerged by the Ocean. 
[128] Pandavas started for their Final End. Parikshit, 36 years old, was coronated on the same day at Hastinapur.
[188] Parikshit ruled for 60 years, coronated his 25 year old son Janmajeya, and died.

Interesting to note, Yudhishthir ruled for 72 years in his 127 years of life!