Nzala is a 21-year-old striker who joined Hayes & Yeading from Cherry Red Records Combined Counties League Premier Division side Southall.
His former clubs include Shoreham, Burgess Hill Town and AFC Varndeanians.
Spiers is a 21-year-old central defender who joins from Sydenhams Football League (Wessex) side Alton FC.
Spiers has also played for Farnham Town.
Myers is a 20-year-old right wing-back who joined Hayes & Yeading from Evo-Stik Southern League Division One South side Fleet Town.
He came through the youth ranks at Hampton & Richmond Borough before spending just over two seasons with Bostik Premier side Metropolitan Police.