I was unable to find sufficient verified information specifically about the Eel River that flows through Clay, Greene, Owen, and Putnam counties in Indiana to write a comprehensive overview. The search results provided contain extensive information about Putnam County's outdoor recreation planning, parks, trails, and natural areas, but do not include specific details about the Eel River itself—such as its origin, flow characteristics, paddling conditions, access points, or other features that would be necessary for an accurate river overview.

The document mentions "Walnut Fork of the Eel River" as being in the southern part of Putnam County, with tributaries including Little Walnut, Warford Branch, and Deer Creek, but provides no additional detail about the river's characteristics, navigability, or recreational opportunities.

Without verified information about this specific Eel River's paddling conditions, water levels, gradient, access points, seasonal patterns, or other essential characteristics, I cannot provide the detailed overview requested. Creating such content without reliable source material would risk providing inaccurate information that could mislead paddlers or outdoor enthusiasts seeking to use this waterway.

To develop an accurate overview of this Eel River, additional resources specifically focused on this waterway in these four Indiana counties would be needed, including paddling guides, USGS water data, Indiana DNR information specific to this river system, or local paddling club reports that clearly identify this particular Eel River tributary of the White River.