The 24th Missouri Infantry was organized from recruits across the state of Missouri, October 24 through December 28, 1861. In 1862 it saw detailed service joining Curtis at Rolla, Mo., January 1862. Curtis' Campaign in Missouri and Arkansas against Price, January to March 1862. Advance on Springfield, Mo., February 2–11. Pursuit of Price into Arkansas February 14–29. Battles of Pea Ridge, Ark., March 6–8. March to Batesville April 5-May 13, then marched to Helena, Ark., May 25-July 14. Duty at Helena until October. Moved to Sulphur Springs, Mo., October 5–11. Pittman's Ferry, Ark., October 27 (3 companies). Moved to Pilot Knob, Mo., October 28–30. March to Patterson November 2–4, to Reeve's Station December 9–10. Return to Patterson December 18. Moved to Van Buren December 21–24, and toward Doniphan January 9–10, 1863.

So, during the period of time the Williams boys joined, the unit was all over the place. Replacements were needed to fill losses regularly. These men were recruited usually in the home areas individual companies were originally raised. Quite often, men were sent home to recruit and enlist men and forwarded to join the unit when a given number of men had been raised.

https://en.wikipedia.org/wiki/24th_Missouri_Volunteer_Infantry

Companies in this Regiment with the Counties of Origin
Men often enlisted in a company recruited in the counties where they lived though not always. After many battles,companies might be combined because so many men were killed or wounded. However if you are unsure which company your ancestor was in, try the company recruited in his county first.

Company A - Captain Thomas A. Reed and Captain John T. Young - Springfield, Greene, Missouri.
Company B - Captain William F. Bodenhamer and Captain Robert W. Fyan - Rolla,Phelps, Missouri.
Company C - Captain Uriah Johnson and Captain Robert Hoggins - Rolla, Phelps, Missouri.
Company D - Captain Charles B. Owen and Captain William Vaughn - Labanon, Laclede, Missouri.
Company E - Captain William W. McCammon and Captain Lafayette M. Rice - Springfield, Greene, Missouri.
Company F - Captain Samson Barres - Rolla, Phelps, Missouri.
Company G - Captain Andrew W. Curry, Captain Charles Dalrymple and Captain James T. Tallaferro - Rolla, Phelps, Missouri.
Company H - captain James J. Lyon, Captain William H. Stark and Captain Isaac B. Tyler - Rolla, Phelps, Missouri.
Company I - Captain Wyatt Harris - Ironton, Iron, Missouri.
Company K - Captain James R. VanZant - Rolla, Phelps, Missouri.

https://familysearch.org/wiki/en/24th_Regiment,_Missouri_Infantry_(Union)