some parts of the two brown splotches south of the Oakland airport are in Hayward. Basically the area around highway 92 / San Mateo bridge, west of 880
Assuming I'm looking at the same thing, it seems like the part relevant to house hunting would be a small area roughly between Grant Ave and Lewelling, which is technically a bit north of Hayward, split between San Lorenzo and San Leandro.
There is also the park/bird sanctuary/landfill near Winton, but that's not residential.
There is also the park/bird sanctuary/landfill near Winton, but that's not residential.