He moved to Pesaro to work under Guidobaldo del Monte, one of the main disciples of Federico Commandino.
He was hired to work in Spain and France as a military engineer, which required him also to help train in the use of artillery.
He returned to the Duchy of Urbino to work as an engineer under the Duke Francesco Maria II della Rovere.
He published his works, prepared in prison, including De gli horologi solari nelle superficie piane (1614, dedicated to Count and Cardinal Teodoro Trivulzio, probably one of his patrons), and a treatise entitled Dello squadro (1625) regarding surveyor's quadrants.
In 1625, Oddi replaced his brother, Matteo, as chief fortifications engineer to the Republic of Lucca.