[xirtamehtsitahw]

Does anyone know what the values are for the analog nub up, down, left or right? Or, if it's even possible to use the analog nub to activate a CWCheat code?

[FAST6191]

I do not believe it is possible. Generally most cheat things like this on whatever system will not have anything for analogue inputs beyond "is it being pressed" -- directions are not just the cardinal directions but some analogue value which can vary between systems a bit and the last thing you want to be doing as a cheat engine maker is coding some kind of dead zone support, analogue value decoders/interpreters or whatever else.

If you are running out of buttons and there is no "is it pressed?" scenario then you might wish to come at it another way and have the game trigger the cheat. Most people do this to dodge issues with game events needing you to run out of bullets/health/stamina/whatever but it works just as well here. A good example might be the game trauma center on the DS -- the game has a miss event and a cheat was made that detected that and refilled the patient health.

[xirtamehtsitahw]

Unfortunately, I'm not well-versed in that sort of cheat hacking. My area of expertise is the various types of known/unknown value searches, as well as memory poking.

How would I go about, say, hacking a code to disable the death routine when one falls into a pit in Super Mario Bros. 3 (being played via my PSP-based emulator, NesterJ v1.13)?

I'd need to re-code that particular part of the game which deals with the death routine, to make Mario reappear at the top of the screen if he falls into a pit, or, somehow enable the "invisible trampoline" effect if he happens to do so (bounce on the "bottom" of the hole). I've never tried to do something of this nature (at least not in an NES game), due to the fact that I can usually achieve what I set out to do with the types of searches/pokes I mentioned in the first sentence of this post.

[FAST6191]

You are using console/firmware (ish) level cheats to hack an emulated title? Such things are not unheard of on the PC (indeed emuhaste and artmoney are often some of the best examples of the cheat making concept) but that is somewhat roundabout.
Some people have toyed with resident memory/generic injection type cheats, as seen in the likes of the GBA and DS with GBAATM and DSATM and prior things, but most hardpatching cheats for older systems tends to be game genie cheats being applied with something like CCCGP.  ( http://s462158067.onlinehome.us/index.php for all of said tools)

Death from pits in SMB3... amusingly mario pit deaths are actually one of the more popular examples of a pitfall in basic cheat to assembly hacks (your basic infinite lives cheat holds a lives counter, you change the death by enemy and it is good, you also have crush, time, possibly environmental hazard and pit that would also tweak that memory location). Though most of that is more concerned with the lives counter rather than some kind of auto respawn.
Anyway back on topic. I am not sure what this game does but what you would want to do there is stop the death from happening and change the OAM height value to the top of the screen or something ( http://wiki.nesdev.com/w/index.php/PPU_OAM ). Doing this on a system that does not copy the binary into RAM is hard but I imagine the ROM ends up in RAM on the PSP so that could work as a poor man's game genie.