We can't easily detect small amounts of deflection in distant parts of the universe because, as you say, we usually have nothing to compare our observations to. (In the case of light being deflected by the Sun's gravity, we can compare how a certain part of the sky looks--i.e., a certain particular grouping of stars--when the Sun is in that part of the sky, vs. when it isn't, and measure the deflection that way. But for light deflection in distant parts of the universe, there's no easy way to do that.)

However, the presence of large amounts of deflection would show up easily: we would frequently see multiple images of the same objects. In fact we only see such multiple images rarely, which indicates that there aren't any regions of large light deflection in our universe.

if for instance the heliosphere had some unknown refractive properties, how could we discover it

The same way we discovered that the Sun's gravity bends light. See above.

That will only tell us about redshift/blueshift; it won't tell us anything about what path the light took to get to us.