We use QCD sum rules to study mass spectra of $P$-wave charmed baryons of the $SU(3)$ flavor $mathbf{6}_F$. We also use light-cone sum rules to study their $S$- and $D$-wave decays into ground-state charmed baryons together with light pseudoscalar and vector mesons. We work within the framework of heavy quark effective theory, and we also consider the mixing effect. Our results can explain many excited charmed baryons as a whole, including the $Sigma_c(2800)^0$, $Xi_c(2923)^0$, $Xi_c(2939)^0$, $Xi_{c}(2965)^{0}$, $Omega_c(3000)^0$, $Omega_c(3050)^0$, $Omega_c(3066)^0$, $Omega_c(3090)^0$, and $Omega_c(3119)^0$. Their masses, mass splittings within the same multiplets, and decay properties are extracted for future experimental searches.
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