Why are alkyl halides used as solvents for relatively non polar compounds and not polar compounds?
Polarity is relative. Dipole moment (macro scale) and dielectric constant of the solvent (molecular scale)  are probably the most decisive. Water has &epsilon;~80, ethanol 25 and DCM is "only" 9. By comparison toluene, benzene or tertachlormethane have &epsilon;~2. The last example also illustrates why differences in electronegativity are not enough. Being symmetric (Td) tetrachloromethane has dipole moment of zero, even if there is a big difference between electronegativity of carbon on chlorine.