Axle seal. Either the seal has a few miles, the front diff got overfilled blowing the seal, or an axle is bent. I haven't tore into the front end yet, but I can tell you it is going to be a job. Plan on doing both sides.
You have a pretty good drip going. I would shut her down and run a backup vehicle. Labor at a dealer is like $40-$60/hr. Might only cost you about $500-700 parts and labor. Find out if they have to order parts.
A forum community dedicated to Dodge Cummins Diesel truck owners and enthusiasts. Come join the discussion about reviews, drivetrain swaps, turbos, modifications, classifieds, builds, troubleshooting, maintenance, and more!