Although many Irish people may be reluctant to acknowledge that our countrymen played a significant role in extending and administering British colonial rule in India, it is a fact that tens of thousands of Irish men (often accompanied by their wives and children) were in India as civil servants with the East India Company and/or India Office (post 1858), or else soldiered there with the regular British army (in the mid-1800s 42% of the British army was Irish), or as part of the EIC's own private armies.
Those wishing to research the history of any Irish family members who served in India should be aware that the archive of the East India Company and the India Office are not held in the National Archives in Kew, but rather are part of the Asia, Pacific and African Collections (APAC) held by the British Library - the limited APAC catalogue (only about 10% of records) is available, however, via the National Archives website: http://www.nationalarchives.gov.uk/A2A/default.aspx
The British library have made a small fraction of their India archive available online at the following:http://indiafamily.bl.uk/UI/Home.aspx but to view most records would appear to involve the hassle and expense of visiting the British Library in London, and this could therefore exclude many people in Ireland, the USA and all the other locations where the Irish diaspora is to be found.
A surprising amount of family history information about British (and Irish) people in India during the 19th Century is, however, available from other internet sources, many of which are free.
A good starting point is the website of the Families In British India Society (FIBIS) http://www.new.fibis.org/ whose volunteers have transcribed several hundred thousand APAC records which can be searched for free here: http://search.fibis.org/frontis/bin/index.php These records include information about ships' passeneger arrivals and departures from Indian ports and the ships' port of origin or destination; birth, baptisimal, marriage, death, burial records taken pricipally from the three Indian Presidencies of the EIC; list of officers and men who served in various military campaigns, or on the establishment of the Presidency armies; biographies etc a typical biography entry may be similar to this one regarding my GGG-Grandfather Robert Xavier Murphy: http://search.fibis.org/frontis/bin/aps_detail.php?id=1048352
The Australian government has digitised the archives of dozens of national, regional and local Australian newspapers, containing several million articles, and made them available free of charge at the following: http://trove.nla.gov.au/ndp/del/home Although not an obvious source for researching relatives who served in India it should be noted that most vessls that sailed, or steamed, to and from Australia in the 19th Century called at India of the way, and so lists of passengers printed in the Australian newspapers also include those travelling to India. During the early part of that era, many official British publications relating to the administration and affairs of its Indian possessions also included information about its Austalasian and Chinese possessions. While these were printed in Indian newspapers, they were also reprinted in Australian newspapers, thus providing information about Indian civil service promotions, dismissals, awards of pensions, granting of leave etc etc This website is, of course, also valuable in researching Irish emigrants to Australia and New Zealand
Similar information is available from the British Library which has digitised many 19th Century newspapers and made them available here: http://newspapers.bl.uk/blcs/ This site is not free but a 7 day pass permitting 200 article views is available for only £9.99 (about 11.50 Euro, or $15.65)
Another excellent newspaper source is The Times of India which has just had its archive from 1838 (when it was the Bombay Times) to 2001 digitised. This has been made available by the company ProQuest and is targeted towards the academic market, so to access it you may need to visit a good public, or university library.
Searching on Google Books will often provide valuable family history materiel given that most 19th Century publications are no longer subject to copyright and have therefore been digitised in full. Publications you can find there relating to India include; Gentleman's Magazine, Asiatic Journal and Monthly Miscellany, Parbury's Oriental Herald, Transactions of the Bombay Geographical Society, Allen's Indian Mail, and Register of Intelligence, Journal of teh Royal Asiatic Society, The Indian Mail: A Monthly register for British and Foreign India, China and Australasia, the Bombay Quarterly Magazine and Review, Alexander's East India and Colonial Magazine etc These publications will provide information about birth's, deaths, marriages, passenger arrivals and departures, military campaigns, military and civil service promotions, society gatherings, court cases, public works and engineering projects etc etc.
Also available on Google Books are several volumes of Hart's Army List aka Hart's Annual Army List, and New Army List, and Militia List. This lists all of the officers and warrant officers serving in all British regiments, including the years each officer was promoted from one rank to another, where the regiment was located, and often includes a small biography of any distinguished officer listing where and how awards, or decorations were won.
Don't forget to consult the Family Search website provided free of charge by the Church of Jesus Christ of Latter Day Saints at the following: http://www.familysearch.org/eng/ as this site includes Indian birth, marriage and death information from official sources (put on microfiche by the Mormons). And the Cyndi's List website http://www.cyndislist.com/ can also provide some useful pointers.