How to improve and maintain technical integrity of a big codebase

Suppose there's a big project (a couple houndred KLOC) that has

• no explicit architecture - everyone can pretty much design stuff however they like


• overall poor design quality (code duplication, weak cohesion, anemic domain model, very mutable types and procedural programming style all over the place)


• low functional and unit test coverage


• a lot of old, potentially unused code


• distributed teams (say, about 30 people total)


• new features are constantly being added, with little thought of how they affect the rest of the code base


• no style guidelines

This kind of works OK for now, but the number of functional defects and regression issues is higher than desired. The effort estimates are typically unpredictable - it's hard to do things properly given all the circumstances described. The amount of re-work is high too.

Is there any particular advice anywhere on how to improve the situation from the technical standpoint? What are the most important steps to focus on in this situation?