If by "older Olympus SLR lenses" you mean a film-era Olympus OM mount Zuiko lens, then you should be able to readily find adapter rings that work for these lenses--but since OM Zuikos are manual-focus lenses, there won't be any autofocus. There won't be any electronic communication from the lens to the camera, so you won't have aperture control from the body, wide-open metering, any shooting modes other than full manual and aperture-priority, and no lens EXIF information when shooting.

However, if by "older Olympus SLR lenses" you mean lenses for an Olympus four-thirds dSLR, then you are out of luck. While the four-thirds mount's registration distance is 38.67mm, plenty large enough to allow adapting to Sony's E-mount's 18mm distance, the problem is that the image circle from any four-thirds lens is only designed to cover a four-thirds sensor (i.e., 4/3"-format sensor). The sensor in a Sony A6000 is APS-C (1.5x crop vs. 2x crop) and is substantially larger, so if you do succeed in mounting the four-thirds lens, it will vignette heavily. The same goes for the m.Zuiko micro-four thirds lenses. And if your lenses don't have aperture rings (i.e., are Olympus, not Panasonic) you won't have any way to control the aperture setting, because there's no electronic communication from the lens to the body.

Keep in mind, too, that there DO exist micro four-thirds to NEX (E-mount) adapters, but these are not for use with regular m.Zuiko lenses, but mostly for manual-focus lenses--most notably, the Samyang/Rokinon 7.5mm f/3.5 Fisheye lens. This is because crazy VR pano shooters like taking fisheye lenses made for a smaller mount, shaving off the hood pedals, and placing it on a camera with a larger sensor for more scene coverage (roughly 180° HFoV), which then requires fewer shots to cover the full spherical view--making it easier to handhold and stitch the panos. This is a very special-purpose type of adapter, and not for general-purpose shooting. And, of course, won't work with four-thirds SLR lenses, only micro four-thirds mirrorless ones.

If you are talking about four-thirds lenses, my recommendation would be to simply bite the bullet, sell them off (if you can) and start investing in native Sony E-mount lenses, or consider switching the A6000 for a Panasonic or Olympus micro four-thirds camera with an Olympus MMF-2 adapter.