What do capacitors C0 and Ce do in this RC phase-shift oscillator?
Those capacitances are part of standard R-C coupled common emitter amplifier. 

\$C_O\$ is coupling capacitor which couples the amplified ac output to next stage/load but blocks the DC bias signal. 

\$R_E\$ connected at emitter improve bias stability by providing a negative feedback (read this answer). But because of this negative feedback the ac signal gain also reduces.

A capacitor \$C_E\$ is connected across \$R_E\$ so that only the DC "sees" \$R_E\$ and hence experiences the negative feedback. Where as the ac signal is bypassed through \$C_E\$ and the gain is not reduced. This capacitor is called bypass capacitor.