A page of spell knowledge essentially adds spells to the bearer's spells known, not to the bearer's spell list
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.