the monster is still alive and attacking, but when you hit with an axe, has the "plink" sound like you are hitting a wall & invincible...

also is "MOVETYPE_PUSH with a non bsp model" is this fixable? 

If you had the "MOVETYPE_PUSH with a non bsp model" error you would know it - the game crashes to console with that text.

My guess is that your oddball monsters come from the following sequence of events:
1) A monster is killed and starts its death animation
2) Another monster wakes up nearby and runs FoundTarget
3) FoundTarget finds the dying monster and changes its animation from dying to running

In step 3 you've quite literally reanimated the dead! When a monster dies, it turns non-damageable immediately, but usually becomes non-solid at some point midway through the death animation. So if you hit the right timing you'd get the behaviour you report. Fix is to exclude dead monsters from the process.