  We detect and characterise extended, diffuse radio emission from galaxy
clusters at 168 MHz within the Epoch of Reionization 0-hour field: a $45^\circ
\times 45^\circ$ region of the southern sky centred on R.~A.${}= 0^\circ$,
decl.${}=-27^\circ$. We detect 29 sources of interest; a newly detected halo in
Abell 0141; a newly detected relic in Abell 2751; 4 new halo candidates and a
further 4 new relic candidates; and a new phoenix candidate in Abell 2556.
Additionally, we find 9 clusters with unclassifiable, diffuse steep-spectrum
emission as well as a candidate double relic system associated with RXC
J2351.0-1934. We present measured source properties such as their integrated
flux densities, spectral indices ($\alpha$, where $S_\nu \propto \nu^\alpha$),
and sizes where possible. We find several of the diffuse sources to have
ultra-steep spectra including the halo in Abell 0141, if confirmed, showing
$\alpha \leq -2.1 \pm 0.1$ with the present data making it one of the
steepest-spectrum haloes known. Finally, we compare our sample of haloes with
previously detected haloes and revisit established scaling relations of the
radio halo power ($P_{1.4}$) with the cluster X-ray luminosity
($L_{\mathrm{X}}$) and mass ($M_{500}$). We find that the newly detected haloes
and candidate haloes are consistent with the $P_{1.4}$-$L_{\mathrm{X}}$ and
$P_{1.4}$-$M_{500}$ relations, and see an increase in scatter in the previously
found relations with increasing sample size likely caused by inhomogeneous
determination of $P_{1.4}$ across the full halo sample. We show that the MWA is
capable of detecting haloes and relics within most of the galaxy clusters
within the Planck catalogue of Sunyaev-Zel'dovich sources depending on exact
halo or relic properties.
