Steger Il Apartments For Rent . The average voucher holder contributes $400 towards rent in steger. The average home rent in steger is $1,171. 3020 Union Ave 1S, Steger, IL 1 Bed, 1 Bath Townhouse 6 Photos from www.trulia.com On average, section 8 housing choice vouchers pay steger landlords $1,200 per month towards rent. Some apartments for rent in steger might offer rent specials. Apartments for rent in steger, il.