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With appropriate interpolating currents the mass spectra of 0+−, 1−+, and 2+− oddballs are studied in the framework of QCD sum rules (QCDSR). We find there exits one stable 0+− oddball with mass of 4.57±0.13GeV, and one stable 2+− oddball with mass of 6.06±0.13GeV, whereas, no stable 1−+ oddball shows up. The possible production and decay modes of these glueballs with unconventional quantum numbers are analyzed, which are hopefully measurable in either BELLEII, PANDA, Super-B or LHCb experiments.