All the technology upgrades I've found have a suffix which seems to determine the tier or effectiveness, such as "Tau" or "Sigma". How many of these tiers are there and which is the strongest?
There are four tiers of tech upgrades: Sigma, Tau, Theta and Omega. Their comparative strengths rank as follows:
Omega > Theta > Tau > Sigma
The stronger the upgrade, the rarer/more expensive the materials required to build it will be, as noted by @David Yell.
As noted by user @SGR, not every tech has four tiers -- four is the maximum you'll see, and the comparative ranks shown above still apply to techs with fewer tiers of upgrades.