I'm making a mod, with a mini quest in it. When playing Morrowind, there are a few quests that, if you kill the NPC, a new journal entry does not pop up and then your stuck with that quest in your list of quests. Then there are some quests where if you kill the npc who gave it to you or who you need to report to, a new journal entry shows up saying you killed so and so and couldn't complete the quest. How do you add a new journal entry on an npc's death?

Use the OnDeath command, and add the correct Jounral index.
example:

Begin "script name"if ( OnDeath == 1 ) 	Journal "name of journal" 30 endif  end

substitute 30 for the correct Journal index.

Attach to the NPC.

I would check the NPC's health:

Begin "script name"short doOnceif (GetHealth < 1 )    if ( doOnce == 0 )        Journal "name of journal" 30        set doOnce to 1    endif endif  end

Fliggerty's CnE mod can cause issues with checking for OnDeath, which is why I recommend GetHealth. It will always work and you don't have to worry about capturing it for that one frame that OnDeath returns a 1.

OnDeath sometimes does not trigger, GetHealth sometimes returns near 0, but still positive integer for dead npc/creatures
I find GetHealthGetRatio/ModCurrentHealth safer, for instance

short doOnceif ( doOnce )  returnendifif ( GetHealthGetRatio <= 0.04 )  ModCurrentHealth -10000   ; ensure health <= 0  set doOnce to 1  Journal "name of journal" 30endif

[EDIT]added doOnce for better working