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 loss
or loses
, etc. then damage reduction abilities can be used.
EDIT:
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.