Spatial walk-off can severely increase the threshold of critical phase-matched optical parametric oscillations (OPOs) and distort the output beam quality. With 16-layer KTP stacks for walk-off compensation, noncritical phase-match-like (NCPM-like) and quasi-phase-match-like OPOs with enhanced angular acceptance have been demonstrated based on two different KTP bonding orientations. In the NCPM-like composite, output pulse energy of $49\mu \text{J}$ has been achieved at pump energy of $523\mu \text{J}$ with pulse duration of 15 ns and repetition rate of 1 KHz. The OPO threshold as low as $254\mu \text{J}$ $\left(44.6\text{\hspace{0.17em} MW}/{\text{cm}}^2\right)$ has been achieved.