How much does the stellar radius change if seen through different filters? I know that the radius of a star should be different depending on the filter being used to do the observation. That is, the bluer the filter, the smaller the measured stellar radius. I know this effect must be pretty small, however, I would like to get more familiar with it. Can anyone point me to some literature or share their own experiences? Would it be a significant difference in Solar radius if we observe the Sun in x-ray vs radio bands?
The "radius" of the Sun is basically where the optical depth to radiation at any particular wavelength is about 1 (or some times 2/3 is used). This is known as the photosphere and is from where the light that we measure comes from.

The "thickness" of the photosphere - i.e. the depth over which the optical depth changes from being negligible to very large is perhaps a few 100 km at optical wavelengths, compared with $7\times 10^{5}$ km for the radius of the Sun. So the exact definition is important at the level of about 1 part in a 1000.

The light coming from the Sun in a "band" is a mixture of light coming from a variety of depths, depending on the exact wavelength. So your question is a bit ill-defined. If we are looking a the wavelength of a prominent absorption line, then the photosphere is higher up in the atmosphere than if we are looking at a  continuum wavelength. The difference is as I say, at most a couple of hundred km.

It's a bit more difficult to define a solar radius in terms of X-ray or radio emission. The Sun is surrounded by a corona that emits radiation at both of these wavelengths, though that plasma is "optically thin" to the radiation. If we were to shine a beam of X-rays or radio waves at the Sun, they would be totally absorbed perhaps about 1000km above where the visible photosphere is defined in something called the chromosphere.

However, the Sun's outer atmosphere (chromosphere and corona) does not have a plane-parallel geometry; it is shaped to some extent by the magnetic field and you can find spicules and prominences that are optically thick that stick up to greater heights in the atmosphere.