You can use SEC/GPC to determine the molecular weight of the polymer. However, depending on the type of polymer you made the accuracy of the measurment would vary. You can use viscometric techniques as Rajyashree has suggested. You can use MALDI depending on how high your molecular weight is. Also you can use light scattering to determine the absolute molecular weight of the polymer.
If your mass is less than 1000 go for FAB-MS other wise you can try MALDI-TOF only thing you have to find out a suitable matrix for ionizing your molecule
For better results if your molecule soluble first do a GPC then go for the MALDI-TOF
As you are mentioning it as an oligomer, if you can form the solution, then Cryoscopy or Ebuliometry are the suitable methods. You can also use Vapour Phase osmometry for the polymers whose molecular weight is less than 25000.