I have added sources.
The The Rosetta Stone for separating the first 4 men named John Budd can be found in Southold Town Records by Anne Winters, 1999
John Budd on:1685/6 : Feb. 13 Southold (This was JB 3 as is seen...)
"Also I doe more perticularly acknowledge to have received from the executors aforesaid full satisfaction for a tract of land left unto my father an in reversion unto me by my Grandfather Mr. John Budd of the Township of Rye, in the County of Fairfield Connecticute of all which legacys and bequests, and of which said sum and sums of money, and more particularly of said aforementioned tract of Lands,.." from Southold Town Records, Vol. 2, p. 255
The second John Budd had died in 1684 and his will names the executors as Isaac Arnold and John Tuttle Sr. These executors had inventories done in both Southold and Rye where John Budd 2nd had homes and land. When John Budd 2 wrote his will he was living in Southold, and owned his father's home and lands in Rye. This second John Budd is mentioned with his father on Januarie 17th, 1658 in The testimony of Richard Case: “John Budd was sayinge hee had beene at the Oyster Pounds:- Thomas Osman asked John Budd if hee saw many hoggs there, or whether hee saw that boore wch you guilt of myne:- that boore saith hee wch I guilt of yors, why is it yors saith hee:- Yes, saith Thomas Osman I mce accompt soe:-I doubt saith Thomas the boore is dead:-No, saith John Budd, I hope hee is good porke:-too:-then Lieutenant Budd answered and said , if it cost me twenty pounds I will have it to New Haven:- you have thus spoken twenty tymes:- I will not have MY SONN thus abused soe whatsoever it cost me:-Januarie 17th, 1658 deposed before me, Barnabas Horton.” Southold Town Records, Vol. 1, p. 468,469
When this deposition was taken, the 3rd John Budd was just 3 days old.
John Budd 3 was born according to Southold Town Records, Vol. 1, p. 463 on Jan 14th 1658. He was 26 years old when his father died and he helped in settling his father's estate. (His sister Ann was born" 1666 Ann Budd borne January the 5th" - Southold Town Records,Vol. 1, p. 465)
This John Budd 3 was known as John Budd, Jr. when on April 28, 1679 (he was 21 years old) Jermiah Vaile, Jr. of Southold, blacksmith, purchased of John Budd, Jr., one-half of Budd's home lot, which Budd states 'was sometime in the possession of my father," consisting of eight acres."
And this John Budd 3 was married by Jan. 13, 1687/8: Deed by John Budd and "Ester Budd, my wife" , to Jona. Horton Wit: David Gardiner, John Pain. Southold Town Records, Vol. 2, p.34
His son, John Budd the fourth was born in 1687 as evidenced by this entry in the Salmon Records:"Mr. John Budd aged 66 (died) Feb. 20, 1753." (1753-66= 1687) Long Island Source Records, Hoff, p.215
This entry was made between the time he wrote his will and the time it was proved.1753-66 = 1687. His will was written Feb 7, 1753 and proved on Jan. 12, 1754. Suffolk Co, New York Will Book Vol. 18, page 492
The first John Budd had died between 1669 and 1673.
The second JB died 1684,
the 3rd John Budd died bet. 1705 and 1727, and
the 4th JB died 1753.
The John Budd who married Mary Prudence Strang was the son of Joseph Budd and Sarah Underhill who married in 1695.
Edited with sources February 8, 2021