The recent advances in autonomous systems have prompted a strong demand for the next generation of adaptive structures and materials to possess more built-in intelligence in their mechanical domain, the so-called mechano-intelligence (MI). Previous MI attempts mainly focused on specific designs and case studies to realize limited aspects of MI, and there is a lack of a systematic foundation in constructing and integrating the different elements of intelligence in an effective and efficient manner. Here, we propose a new approach to create the needed foundation in realizing integrated multifunctional MI via a physical reservoir computing (PRC) framework. That is, to concurrently embody computing power and the various elements of intelligence, namely perception, decision-making, and commanding, directly in the mechanical domain, advancing from conventional adaptive structures that rely solely on add-on digital computers and massive electronics to achieve intelligence. As an exemplar platform, we construct a mechanically intelligent phononic metastructure with the integrated elements of MI by harnessing the PRC power hidden in their high-degree-of-freedom nonlinear dynamics. Through analyses and experimental investigations, we uncover multiple adaptive structural functions ranging from self-tuning wave controls to wave-based logic gates. This research will provide the basis for creating future new structures that would greatly surpass the state of the art - such as lower power consumption, more direct interactions, and much better survivability in harsh environment or under cyberattacks. Moreover, it will enable the addition of new functions and autonomy to systems without overburdening the onboard computers.