From my own experience, this can be elucidated through size-exclusion chromatography ie. gel filtration - aggregation usually elutes in the column void volume. Also folded and unfolded proteins have differences in their gel filtration retention. Additionally you can couple static light scattering (SLS) to get information regarding oligomerization and later analyze your fractionated sample with circular dichroism (CD) to distinguish between folded and unfolded species. The amount/percentage of each oligomer/fold species you can get from your gel filtration chromatogram by peak integration.

The secondary structure contents of your samples can be avaluated by circular dichroism in the UV range; I doubt whether you can mount it on a reactor though. I also root for a GPC/SLS/UV setup if you can get your hands on one.

Besides the suggestion given above using ANS (1-Anilinonephthalene Sulphonate) could be a good idea. This dye binds to hydrophobic sites and fluoresce nearly 350nm. So fluorescence intensities will be different at native, unfolded and aggregated state. Measuring hydrodynamic radii of the molecule with DLS could be another way, as it differs during unfolding and aggregation. measuring turbidity by absorbance at 350nm can also be used, if your lab is too ordinary to work with.