It looks like Thomas Wasden, Sr. was granted a headright grant of 450 acres in Burke County, Georgia in 1790. Jefferson County wasn't formed until 1796. (He must have had a large family then because most of the grants were around 150.
He is on the earliest tax digest of 1794 owning 450 acres and Thomas, Jr. is also on this list owning no land but taxed 1 poll. In 1799 an Elijah Wasden is added with no land to Jefferson County. Elijah is never shown again and I give warning that many times Walden and Wasden were interchanged. This Elijah may have been a Walden but it is unknown.
By 1803 Thomas, Sr., Thomas, Jr. and William are shown in Jefferson County, next door neighbors to the Walden's. Jefferson County bordered Warren County and William was listed in Warren County in 1805 still with no land. He must have been in his mid 20's just guessing.
Thomas, Sr. is listed as Parent of Elizabeth Wasden in 1812 so his wife must have died. I don't know who she was. A Phillip M. Wasden is on the tax list by 1815. The prior year in 1814 Thomas, Jr. filed as Admn. of Thomas Sr's Estate so he must have died in 1813. I would guess that Phillip may be Thomas Jr.'s son.
There are several Wasden marriages recorded in Jefferson County but most after 1815. One marriage Eli Wasden to Sara Pilot in 1815 is believed to be our Eli Walden as his wife is shown as Sara on the 1850 census and this would be about the right age for our Eli to marry - and based on his first son's birth. Sara Pilot's sister married Robert Pittman and Robert filed for Eli Walden on several tax digest's hence this decision.
The Walden and Wasden's floated across the Warren line during these early years and looks like William must have been there alot as not many records in Jefferson. Unfortunately Warren County does not have but a handfull of tax digests that were saved.
I may have more info once I check my sources if you want to contact me by email at firstname.lastname@example.org