"General big blur" -- what do you mean?Don't forget certain games add artificial motion-blur, so you also want to turn that off those settings.
If that is not the issue -- Are you familar playing on old-style CRTs? Do you see the same issues you describe when playing on CRTs?
If you never have seen the issue when playing on a CRT -- are you describing something else other than blur? Are you talking about haziness (e.g. poor blacks instead of blur) -- that's normal with some strobed LCDs, especially TN LCDs, since they are running at more aggressive LCD-refreshing settings, and that can impact color quality. A different strobed display (non-TN) can reduce or eliminate this compromise.
Alternate possible cause -- A framerate mismatch with refreshrate can create more blurry impression, much like the lower framerate UFOs at http://www.testufo.com
do not look as clear as the higher framerate UFOs. In fact, mismatches like 129fps@120Hz or 153fps@120Hz can also create blur-by-stutter effect, slightly reducing motion clarity at odd frame rates higher than refresh rate. Certainly not as bad as 30fps@60Hz or 60fps@120Hz, but super-rapid microstutters can and do blend into a form of slight blurring. Especially if the beat frequency and harmonics between the framerate-refreshrate is very high; the vibrations of stutter is so high, it blends into slight blur. Blur-by-rapid-microstuttering: Is this the "blur" you are talking about?
Strobing turned on can indeed work at its very best with VSYNC ON -- but that can add the latency issue. (And stutters, if your GPU isn't powerful enough to keep framerate locked at all times). For the best strobing clarity and motion perfection, Strobing + framerate locked + VSYNC ON + 1000Hz mouse. Framerate always matching refresh rate matching strobe rate.
Frame rate capping can also be a reasonable lower-lag substitute for VSYNC ON, but with pros/cons.
While good for motion clarity, it's not always ideal for input lag (...VSYNC ON + strobing usually has too much lag for competition players...). But that doesn't matter in many games where you can benefit from motion clarity.