I am curious to know if a reverse osmosis system can clean water from radioactive elements like cesium-134 and cesium-137. If it can, how efficient can it be?
I don't know about cesium in particular, but according to the EPA's web site (see the section called "How will radionuclides be removed from my drinking water?"), both isotopes should be covered under the beta particle section.
I cannot quantify the efficiency part of your question, but presume it's acceptable to the EPA (which may or may not instill confidence to you in terms of whatever methodology they're using).
The following treatment method(s) have proven to be effective in removing radionuclides at levels below their MCLs:
Beta particle and Photon Radiation: ion exchange and reverse osmosis;
(Gross) Alpha Emitters: reverse osmosis;
Radium 226 and Radium 228 (Combined): ion exchange, reverse osmosis, lime softening;
Uranium: Ion exchange, reverse osmosis, lime softening, coagulation/filtration.
Radioactivity does not apply so much to an element as it does to a specific isotope of that element. Many elements have both radioactive and non-radioactive isotopes. In general, if a reverse osmosis membrane removes a particular element or compound it will remove all isotopes of that element to a similar degree.
"The best solution may be the one used routinely to treat water at the Savannah River Site. The process combines activated carbon, reverse osmosis, and ion exchange. If one doesn't get the iodine-131, two others have a chance to capture the radiation through other means." https://www.forbes.com/sites/jeffmcmahon/2011/04/07/how-to-remove-radioactive-iodine-131-from-drinking-water/#18325ad52a66