Pilot reported a near midair collision that required evasive action while practicing an instrument approach and observed the other aircraft fly erratically; causing other airborne conflicts within the traffic pattern.

Narrative

The event happened during a practice flight in my aircraft. The purpose of the flight was to practice some checklist items subsequent to me finishing my instrument rating; and to help my instructor maintain instrument currency. The flight took place with my instructor (who at the time was not formally providing instruction) flying using a view limiting device from the right seat and me sitting in the left seat acting as safety pilot and pilot monitoring. We were practicing the ILS 32 approach to OKV in VMC conditions. We made numerous traffic calls; and at times would break off the practice to allow incoming traffic that was faster to come in without having to go around us. We heard among others a single radio call from Aircraft Y reporting a position near the field; and we determined that they would be no factor. We continued the approach and I continued looking for traffic. We then saw a ADS-B return from Aircraft Y very close to our position; and we immediately began looking for the traffic; and taking evasive action by side stepping to the right. At the same time; a friend in an aircraft on the ground made a radio call warning us that it appeared that Aircraft Y was 'right on top of us' and to break off. We then observed Aircraft Y make several erratic maneuvers directly over the airport at or about traffic pattern altitude including a right (non standard) pattern; and an erratic entry to reenter the left downwind for Runway 32. At least one other aircraft had to take evasive action. After we verified that we were clear of conflict; we called Aircraft Y on the radio but the pilot did not respond nor make any further radio calls. There were at least 3 other aircraft in the pattern or vicinity of the airport at this time. My instructor and I debriefed the incident and discussed the importance of situational awareness; communication in a busy pattern; and correct pattern entry procedures.