I'm gonna throw some text at you (emphasis mine)
From the text on Necronomicon:
Exhaust and spend 2 movement points to make a Lore (-2) check. If you pass, draw 1 Spell and lose 2 Sanity. If you fail, nothing happens.
From the text on Elder Sign:
When sealing a gate, lose 1 Stamina and 1 Sanity and return this card
to the box. You do not need to make a skill check or spend any Clue
tokens to seal the gate. In addition, remove one doom token from the
Ancient One's doom track.
From Harvey's Strong Mind ability:
Strong Mind - Any Phase: Harvey reduces all Sanity losses he suffers by 1, to a minimum of 0.
From the 'Casting Spells' section of the AH rulebook:
Every spell has a casting modifier, and most have a Sanity cost
And finally from the Fantasy Flight FAQ:
Q: Does the Strong Mind ability (reduce all Sanity loss
by 1) of the professor, Harvey Walters, apply to the casting of spells?
A: No. The professor’s ability works on losses, not costs.
The same distinction applies to the gangster, Michael
McGlen, and his ability to reduce Stamina losses.
I can see where'd you be confused due to the wording in the DH rulebook, but Harvey would reduce the sanity loss from both tomes and the Elder Sign. It's a fine line between paying some price in order to activate some ability and losing something due to activating some ability. If the text in question specifically states
loses, etc. then damage reduction abilities can be used.
For an additional example of cost vs. loss, consider the card 'Pentagram of Blood' from the Curse of the Dark Pharaoh expansion:
Discard this card and X Stamina to ward your current street.
Or from the revised edition:
Spend X Stamina and discard this card
Loss of staminia isn't explicitly called out in either of those ability descriptions. You could almost break it down as a 'Do X to do Y, then Z'. The necronomicon is '..spend 2 movement...to make a Lore (-2) check...then lose 2 sanity'. This wording structure won't work all the time, but hopefully it'll aid in determining when damage reduction abilities can apply.