How loud do you have to have your amp to get these to sound?

I may be doing them incorrectly but I really don't hear much most of the time without actually plucking/pickin the string
you're doing it wrong. push harder and articulate you fingers more.
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So if done correctly, without actually picking the string with my right hand... I should hear an audible sound equivalent to that of a picked note?
It'll be quieter then a picked note, but you should be able to do it on an acoustic with no problem. Either an acoustic or an electric unplugged.
the hammer-ons should be slightly less audible than a picked note, also not as clear, but the pull-off should sound the same as a finger picked note
unless your doing a hammer on from the 5th fret to the 12th fret with your index finger and pinky, it shouldnt be too hard. just do what it means, hammer on with your finger. as far as amp settings, the more distortion, the more audible hammer ons and pull offs will be.
try this

1 string e - 3h4p3
2 string b - 3h4p3

1 string e - 3h4h5p4p3

so on and so forth.

EDIT: when pulling off, rip your finger down off the string hard, but keep it in place with the stationary finger.
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yeah, you should be able to hear it on an acoustic or clean. thats if your doing it properly
haha i can hammer from 5th to 12th with only slight difficulty seltzer

and it sounds almost the same volume
(my hammers and pulls are always only ever so slightly quieter unless my fingers are tired)
Overdrive help, but like the guys above, it must sound on clean. Remember, when you pull off, you try to hit the string with you finger like pushing/bendind it down (left hand).