  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 $4.57 \pm
0.13 \, \text{GeV}$, and one stable $2^{+-}$ oddball with mass of $6.06 \pm
0.13 \, \text{GeV}$, 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.
