I have a few more resources found in libraries where Joseph Burke is mentioned. Just this afternoon I found a listing of his service in the War of 1812 and that of his two sons, Aretas and Silas Burke:
Page 103. Vol. 1.
. ROLL OF CAPT. HARVEY MURRAY'S COMPANY.
(Probably from Cuyahoga County.)
Served from August 21,, until November 30, 1812.
I found more information on his War of 1812 experience:
From Historical Collections of Ohio
By Henry Howe
The First Militia Muster in Cuyahoga county was held on the 16th of June, 1806,
…at DOANE’s Corners. Nathaniel DOANE was captain; Sylvanus BURKE, lieutenant; and Samuel JONES, ensign, with about fifty privates. The surveying party being at Cleveland, and many strangers, this event attracted much attention. Never had so many whites been collected together in this vicinity as on this occasion. The military marched and countermarched to the lively roll of the drum of Joseph BURKE, who had been drum major in the Revolution, and the soul-stirring strains of the fife of Lewis DILL. “Yankee Doodle,” “Hail Columbia,” and “Who’s Afeared” were among the tunes that aroused the martial spirit of many a gallant heart, as he wielded, perhaps, some ancient relic of the Revolution upon his shoulder.
The last pieces of information that I have been able to find on Joseph Burke are
from “History of Lorain County, Ohio with Illustrations & biographical sketches of some of its prominent men and pioneers.” Publ 1879:
Page 149 in section on Columbia Township
“Joseph Burke was the earliest settler in Euclid
. He came from New York in 1798, traveling from Buffalo to Grand River in an open boat. Leaving his family there, he came on to take a look at the wilderness, in which he thought of settling, and after making a selection at Euclid, returned for his family. He resided in Euclid eleven years, and then removed to this township, locating on lot twelve (1809? Srb). He died July 4th, 1814. His widow removed to Michigan, and died there in 1832. Of their large family of fourteen children, only two are living: Ira Burke on the old homestead, aged seventy-five, and Mrs. Sophia Lender, residing in Illinois. A little daughter, four years of age, while in the woods with her brother, who was making maple sugar, wandered away and was never found. The generally accepted theory as to her fate is, that she was carried away by Indians seen in the vicinity a day or two previous.”
Page 152, in Methodism
…The first Methodist services held in town were at the home of the Widow of Joseph Burke, in about the year 1818. Following members…Mrs. Joseph Burke and her two sons, Allen and Orrin…
Page 154, in The Militia
In the year 1810, a company of militia,composed of men from the townships of Columbia…The following are the names of the members: Joseph Burke…Chauncey Warner…
Page 155, in The Block House
“In the spring of 1812, Benoni Adams, while in search of some cattle, spied Joseph Burke as he was getting over a brush fence some distance from him, and it occurred to Adams to have a little sport. Evidences of Indians in the immediate vicinity had recently been seen, and, when Adams gave a shout in the imitation of the Indian’s warwhoop, Burke darted off like a deer for his house. Adams, seeing his fright, and fearing the consequences of his joke, called after him to stop, but the only frightened Burke the more. Arriving at the house, he apprised his family of their danger, and with their youngest child in his arms, Mrs. Burke following with the rest, set out for the fort, Burke yelling “Indians!” all the way. The alarm spread rapidly, and many ludicrous scenes were enacted.”