Dynamic light scattering (DLS) is used in Molecular Weight determination in some situations. Please search relevant literature to see if this technique can be applied in the Molecular Weight regime you are interested in measuring.

You can use SEC, which is done with HPLC / ELSD, you only have to buy a SEC column suitable for the molecular weight of your sample

Oligomers of what? If they are soluble in, say, methanol, you should definitely do MS. Mass of 1000 is reasonably low, so electrospray should work fine if whatever you're working with can be ionized in one way or another.

MALDI-TOF. If there is a marker, NMR is a very good choice.