The arrival of the two 19-year-olds takes Saddlers boss Mat Sadler's summer haul of signings to 12.
Former Manchester City academy product Griffiths is on his first loan move.
Okagbue spent the first half of last season on loan with National League side Oldham Athletic.
He also had a loan spell at sixth-tier side Chester in the 2021-22 season.
The five-times capped Republic of Ireland Under-19 international could figure at home to Colchester United on Saturday, but Griffiths appears to have been signed too late to figure.
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