How were these organised into Divisions, Grand Divisions or battalions?
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
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):
REGIMENT, (regiment, Fr.) a term applied to any body of troops, which, if cavalry, consists of one or more squadrons, commanded by a colonel; and, if infantry, of one or more battalions, each commanded in the same manner. The squadrons in cavalry regiments are divided, sometimes into six, and sometimes into nine troops. The battalions of British infantry are generally divided into ten companies, two of which are called the flanks; one on the right consisting of grenadiers, and another on the left formed of light troops. There is not, however, any established rule on this head; as both cavalry and infantry regiments differ according to the exingencies of service in time of war, or the principles of economy in time of peace. We are humbly of opinion, that every regiment of foot should consist of 2400 men, making three battalions of 800 each.
the companies would have irregular sizes, from the same volume:
COMPANY, in a military sense, means a small body of foot or artillery, the number of which is never fixed, but is generally from 50 to 120, commanded by a captain, a lieutenant, and an ensign, and sometimes by a first and second lieutenant, as in the artillery and flank companies of the line. A company has usually 3 or 4 serjeants, 3 or 4 corporals, and a drums. In the guards the companies consist of 120 men each, as in the artillery.
You can refer to the same source for other such information.