Intermolecular Forces

(The above picture also shows the polarity of the bonds in the individual molecule as well.) 

If two Dimethyl Sulfoxide molecules were attracted to each other, Dispersion forces and Dipole-Dipole forces would occur. 

London Dispersion forces act on all molecules, it does not matter if it is a nonpolar or polar  molecule. Dispersion forces occur when there is an attraction between temporary or induced dipoles in adjacent molecules. It is a temporary dipole. London dispersion is caused by the movement of electrons around the two atoms, one end of a polar molecule can be temporarily positive and another end may be temporarily negative. In DMSO it occurs between the atoms. 

Dipole Dipole occurs in all polar molecules. Adjacent molecules line up so the negative pole of one molecule is as close as possible to the positive pole of its neighbor. It is a electrostatic attraction. Oxygen is more electronegative than Sulfur; therefore a dipole can be created between a Sulfur of one molecule and Oxygen of an adjacent molecule. (This is indicated by the dotted line) 

There is no Hydrogen bonding because Hydrogen bonding is a specific type of dipole-dipole where a bond is formed between a Hydrogen atom and a Nitrogen, Oxygen, or Fluorine atom. Hydrogen bonding is a special type of the dipole-dipole attraction.  This does not occur in DMSO. As mentioned in the introduction, DMSO is an aprotic solvent. An aprotic solvent is a solvent that has ion dissolving power but lacks an acidic hydrogen, which is a hydrogen that can be donated to another molecule. Thus, it cannot have hydrogen bonding.