Short answer is No
From the description of the spell:
The subject is immune to all death spells, magical death effects,
energy drain, and any negative energy effects.
This spell doesn’t remove negative levels that the subject has already
gained, nor does it affect the saving throw necessary 24 hours after
gaining a negative level.
Death ward does not protect against other sorts of attacks even if
those attacks might be lethal.
Okay, so in order to be protected the effect has to either
- Have the [death] descriptor
- Be a magical death Effect
- Cause energy drain (usually negative levels)
- Be a negative energy effect
So, from your examples,
- Venom - Nope, not at all.
- Necromancy Spells - Not usually, unless it meets one of the 4 above
- Other - Nope, unless it meets one of the 4 above.