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3rd Gen Ram Tech2002-2008 Rams: This section is for TECHNICAL discussions only, that involve the 2002 through 2008 Rams Rams. For any non-tech discussions, please direct your attention to the "General discussion/NON-tech" sub sections.
Are you sure it is oil burning or is it exhaust fumes? If it is exhaust, you might have an exhaust leak. If it is oil, you have oil dripping on the exhaust somewhere. Oil usually won't burn unless it is hitting something pretty hot, like the exhaust. Most likely place is the valve covers leaking on to the exhaust manifolds. Hope this helps.