Appalachian dialect equivalent of "Hollow," a narrow valley typical in the region. The full line means that he's stealthy going through the said hollow.
Appalachian dialect for "swallow." The full line being "Give me a swallow" refers to the moonshine that Dooley produced.
A law officer or governmental official that dealt with moonshiners & illegal alcohol (prohibition-era term).
An imperial measurement. 1 tun is equal to 252 gallons. Not to be confused with a ton (a weight measurement).