converting a nine speed hybrid disc to a seven speed drop bar, is it possible?
The Coda's freehub body can take a 7-speed cassette with the addition of a 4.5mm conversion spacer to take up the extra room, which is a common bike shop item.

There are two stumbling blocks though.

First, if the Coda's current left shifter and front derailer come from a Shimano mountain group, which they probably do, then they won't work correctly with STI because the actuation ratio is different between mountain and road. It can be made to work badly but will never be right. So if this is what you have (as opposed to a flat bar road shifter and a road derailer), you'll need a road derailer, and then there's the question of getting one that either plays nice with the existing crank or getting a crank to match it. If you don't want to have to mess with changing cranks, you may look at the IRD Alpina FD, because it's just about the only one out there that has a cage profiled for mountain/hybrid/trekking/etc triples and takes road cable pull.

Second, you probably have normal v-brake-lever-compatible brake calipers, whereas your STIs have road/sidepull/canti cable pull. They don't work together, at all. So you need either road calipers or a cable pull conversion device such as Travel Agents.