Could not establish a family connection between the various Gallaghers. This is what I did find

Gallagher, Daniel of Milwaukee, Wis., c.1847 born; April 18, 1864 pvt., Co. D, 17th Wis. Infantry Rgt. July 22, 1864 severely wounded in right forearm at Atlanta, Ga. July 4, 1865 discharged for wounds.
Possibly born in Massachusetts, son of Edward and Catharine Gallagher and as of 1850 and 1860 living at Clymer, Wis. With parents

Gallagher, Hugh of Clinton, N. Y. Feb. 13, 1862 pvt., Co. B, 17th Wis. Infantry Rgt. March 31, 1864 found dead at Chicago, Ill. City Hotel

Gallagher or Galligher, James of Fond Du Lac, Wis. c.1823 born in Ireland; Feb. 24, 1862 pvt., Co. C, 17th Wis. Infantry Rgt. no date wagoner; Aug. 23, 1864 wounded at Atlanta, Ga. July 14, 1865 mustered out at Louisville, Ky. Dec. 1, 1877 applied for a pension (certificate #160331); 1880 farmer at Friendship, Fond Du Lac County, Wis. March 19, 1888 his widow Rosa Gallagher (c.1825 born in Ireland) applied for a pension while living in Wisconsin (certificate #316253); Children: Joseph Gallagher, c.1858 born, Sarah Gallagher, c.1866 born, Frank Gallagher, c.1867 born, and Willie Gallagher, c.1869 born, all children born in Wisconsin

Gallagher, Martin of Madison, Wis. Dec. 4, 1862 pvt., Co. B, 17th Wis. Infantry Rgt. July 14, 1865 mustered out at Louisville, Ky.

Gallagher, Owen of Russell, Wis. Oct. 18, 1861 pvt., Co. E, 17th Wis. Infantry Rgt. July 14, 1865 mustered out at Louisville, Ky.

Gallagher, Patrick of Franklin, Wis. Dec. 14, 1861 pvt., Co. K, 17th Wis. Infantry Rgt. May 22, 1863 wounded at Vicksburg, Miss. July 14, 1865 mustered out at Louisville, Ky. Nov. 10, 1883 applied for a pension while living in Wisconsin (certificate #400167); 1890 living at Chelsea, Taylor County, Wis.
PROBABLY SAME MAN--Patrick Gallagher, c. 1826 born in Ireland; as of 1880 deputy sheriff at Marinette, Marinette County, Wis., single and living his a younger brother John and John's family

Gallagher or Galigher, Peter of Westport, Wis. Jan. 28, 1862 cpl., Co. F, 17th Wis. Infantry Rgt. Oct. 3, 1862 wounded at Corinth, Miss. no date sgt. Jan. 8, 1863 died at Lake Providence, La.

Sources: Roster of Wisconsin Volunteers: War of the Rebellion; The Medical and Surgical History of the Civil War; Pension Index; 1880 U. S. Census; 1890 U. S. Veterans Census