Flight Instructor with student reported a NMAC during final approach at a non-towered airport with an aircraft that performed a non-standard pattern entry. The Instructor took evasive action to avoid a collision.

Narrative

My student was flying the RNAV 14 approach into HII. I made radio calls stating that we were inbound from the EED VOR; approximately 10 miles out on final. I continued making position reports: 8 miles; 4 miles; and 2 miles straight in for Runway 14. Another aircraft on frequency asked for our speed to determine spacing; and I advised we were at 80-90 knots on final. They responded that it shouldn't be a factor.When we were about 1.5 miles from the runway; I saw Aircraft Y on base; headed directly toward us. I announced their callsign over the radio; but there was no response. They seemed completely unaware. To avoid a mid-air collision; we diverted to the right; as there are mountains to the left of the runway. I made another call stating; 'Making a right turn to avoid traffic that just cut us off on final;' but there was still no response from them.We continued flying toward the lake; then re-entered the downwind at a 45-degree angle to make right traffic for Runway 14. Upon reviewing Aircraft Y's flight path; I saw that they had flown in from ZZZ and entered directly on base. Aircraft Y could have entered from the downwind to better sequence with other traffic.