How were these organised into Divisions, Grand Divisions or battalions?
A traditional British regiment was divided into 3 battalions. A standard battalion had nominally 800 foot soldiers. A standard regiment, 2400 soldiers. Quoting from "A New and Enlarged Military Dictionary" by Charles James (1802):
the companies would have irregular sizes, from the same volume:
You can refer to the same source for other such information.
Having dug out Lineage Book of British Land Forces 1660-1978, Volume 2 (Frederick 1987) from the library, I have discovered that that the nominal strength of a regiment of foot in 1775 was 737 men. Regiments were composed of 10 companies: 8 battalion companies, a grenadier company and a light company. A full strength company would consist of 3 officers (usually a captain and subalterns, either lieutenant or ensign rank), 2 drummers (fifers in grenadier companies), 6 NCOs (2 sergeants) and 62 private soldiers. The regiment general staff would make up the rest.
During the 'American War' some regiments were granted a further 2 companies for recruitment purposes, bringing their upper limit to 811. Guards regiments sometimes had larger companies of 100 or more.
However, at the start of the war, the average regiment consisted of only 477 men - particularly if on service in the English Establishment (other territories varied further). Grenadier and light companies were detached to form their own battalions (such as the famous 'bloodhounds' of the 2nd Battalion of Light Infantry) which further reduced regimental numbers. Quite often, regiments were split across barracks and rarely paraded together, which compounded recruitment problems (it was a volunteer army). It also made large scale military manoeuvres difficult, to the point that regiments were having to train together for the first time in the theatre of war. (Houlding 1981, Spring 2010 - see below)
According to the Manual Exercise 1764 (last printed in 1778), each company would form a subdivision, 2 companies form a grand division. The Battalion is formed of several grand divisions.
Divisions were formed to perform the firings. In the exercise, mass firings (three ranks firing by battalion) were practice. However, in America, General Howe countermanded these orders and instructed divisions to fire in the alternate fire method used by Wolfe in the French and Indian Wars. Further to this, divisions would form in 2 ranks at open order and fire by company, giving the captains and subalterns significant initiative.
To complicate matters of regimental strength further, due to the lack of cavalry and broken, rough terrain in America, the usual European Order of Battle was distilled into smaller, more mobile forces with detachments and transfers commonplace, particularly for flank units.
Houlding, J. A (1981) Fit for Service: The training of the British Army, 1715-1795 Spring, M (2010) With Zeal and Bayonets Only: The British Army on Campaign in North America, 1775-1783