  We examine gravitational waves (GWs) emitted from axionic strings and domain
walls (DWs) in the early universe using advanced 3D lattice simulations. Our
study encompasses scenarios for domain wall numbers $N_{\rm DW}=1$ and $N_{\rm
DW}>1$, which correspond to GWs primarily from strings and DWs, respectively.
Simulations begin before the Peccei-Quinn (PQ) phase transition and conclude
with the destruction of string-wall networks below the QCD energy scale,
relevant to both QCD axions and axion-like particles (ALPs). For $N_{\rm
DW}=1$, the GW energy density from axion strings appears undetectable for both
QCD axions and ALPs. In contrast, for $N_{\rm DW}>1$, the GW spectrum is
largely determined by the bias term's coefficient, with the QCD axion model
predicting undetectable GW emissions, while the ALPs model allows for a
detectable GW signal in the nano-Hertz to the kilo-Hertz frequency range.
