This is the 768th most frequent Finnish word.
omia
"Omia" means "one's own" in English.
In this sentence, 'omia' (used here as 'omista', its partitive form) emphasizes the possessiveness and individuality of the hobbies.
Pidän omista harrastuksistani.
I like my own hobbies.
Here, 'omilla' is the plural adessive form of 'omia', indicating methods personally particular or belonging to the person referred to.
Hän haluaa tehdä oman työnsä omilla tavoillaan.
He wants to do his job in his own ways.
In this usage, 'omilla' (plural adessive) emphasizes possession and specifies the toys as those belonging to the children themselves.