In a current campaign I am playing a sorcerer/oracle. If I have a page of spell knowledge with a divine spell on it, can I use my arcane slots to cast it?
The page's description says:
If the bearer is a spontaneous spellcaster and has that spell on her class spell list, she may use her spell slots to cast that spell as if it were one of her spells known
The page of spell knowledge says, "If the bearer is a spontaneous spellcaster and has that spell on her class spell list, she may use her spell slots to cast that spell as if it were one of her spells known."
Thus, if the bearer of the page is a sorcerer and has that spell on her sorcerer spell list, she can use her sorcerer spell slots to cast that spell as if it were one of her sorcerer spells known. Likewise, if the bearer is an oracle and has that spell on her oracle spell list, she can use her oracle spell slots to cast that spell as if it were one of her oracle spells know.
However, if the bearer of the page is a multiclass oracle/sorcerer and has that spell either only on her oracle spell list or only on her sorcerer spell list, she does not have the spell on that other spell list, and she's stuck casting the spell using the spell slots of whatever spellcasting class does have that spell on its spell list.
The page of spell knowledge doesn't change the sorcerer's spellcasting that says, "A sorcerer casts arcane spells drawn primarily from the sorcerer/wizard spell list," nor does the page change the oracle's spellcasting that says, "An oracle casts divine spells drawn from the cleric spell lists." If a spell's not on a class's list, that class's spell slots can't typically be used to cast it, even with the help of a page of spell knowledge.
Divine and Arcane classes doesn't naturally share their spell-slots
As Hey I Can Chan's answer explains, Sorcerers and Oracles cast their spells from different spell lists and then prevent you to use the spell slots of one class for another.
However a way to solve this issue would be the Mystic Theurge class, which allows to share the spell slots for spontaneous-caster classes, as explained in Paizo FAQ with an oracle/sorcerer/mystic theurge example:
Likewise, an oracle/sorcerer/mystic theurge can use sorcerer spell slots to cast oracle spells, or oracle spell slots to cast sorcerer spells, so long as the level increases and level limits described in the combine spells ability are implemented. Neither class is affected by the "only spells they have prepared" rule because that rule only applies to mystic theurges who have levels in a non-spontaneous casting class.
