How strong does one generally have to be to compete at elite level at judo?
Judo Australia has published the following strength and fitness guidelines for its cadet judoka (lifts in terms of 3 rep max):
In this document are a series of tests you can use to check your progress with Gold, Silver and Bronze targets that are based on the standards achieved by elite Australian and International cadet judo athletes. The Bronze targets are the minimum standards that you should be attaining in order to consider yourself a high-performance Australian judo athlete.
The following website (link dead) had a similar breakdown of core strength exercises in three skill bands (data taken from this site, lifts in terms of 1 rep max):
The German Judo Federation gives a similar list of benchmarks for elite performance: