The correct order of increasing boiling points for the given compounds is:

C2H6 < CH3Cl < C2H5Cl < CH4

This is because boiling points are largely determined by the strength of intermolecular forces between molecules. As the molecular weight of the compound increases, the strength of the intermolecular forces also increases, leading to a higher boiling point. Additionally, polar molecules tend to have higher boiling points than nonpolar molecules of similar mass because of the presence of dipole-dipole interactions.