Omega is the ratio of the actual effective mass density in the universe, to the critical mass density set by the value of Hubble's Constant.
The best way to get Omega I know of, is to measure the Hubble Constant at the largest scales comparable to the curvature scale of the universe, about a redshift of 0.5 to 1.0. This gives you the critical density of the universe. After allowances are made for local 'flows' and anisotropies, tells you the critical density of the universe from H^2 = 8 pi G Rho/3 where Rho, the total mass density needed from all contributions such as matter, radiation, dark matter and the cosmological constant.
Next, you need to determine what the magnitude of the deceleration parameter, which is the rate of change in time of the Hubble's Constant. If it is smaller than the rate determined from the critical density, then thee universe will expand indefinitely. If it is large, the universe will recollapse. This is, effectively, a measure of the actual density of the universe relative to the critical density or Omega. Presumably, by measuring Hubble's Constant for a range of distances intervals out to a redshift of 1.0 or more, you can determine the deceleration parameter exactly and unambiguously. The best way we know how to do this is by using Type 1A supernova in distant galaxies to determine Hubble's Constant.
All other tests involving element abundances, gravitational lensing and the like, merely help us distinguish between the various contributions to Omega in dark matter, baryons, and the cosmological constant, and are fraught with a variety of difficulties. Currently, there are over a dozen different methods that have been used to estimate Omega. The vast majority show Omega less than unity by factors from 2 to 10 suggesting a simple, open universe, and one in contradiction with Inflationary cosmology.