Two undescribed p-terphenyl derivatives, asperterphenylcins A–B (1–2), and two undescribed diphenyl ether derivatives, asperdiphenylcins A–B (3–4), together with three previously described p-terphenyl derivatives—4″-deoxyterprenin (5), terphenyllin (6), and 3″-hydroxyterphenyllin (7)—were obtained from the solid-rice culture of the marine-derived fungus Aspergillus candidus HM5-4, which was isolated from sponges from the South China Sea. Their structures were elucidated by HRESIMS data and NMR spectroscopic analysis. Compound 1 showed a strong inhibitory effect on Neoscytalidium dimidiatum, with an inhibition circle diameter of 31.67 ± 2.36 mm at a concentration of 10.0 µg/disc. Compounds 5 and 7 displayed cytotoxic activity against human chronic myeloid leukemia cells (K562), human liver cancer cells (BEL-7402), human gastric cancer cells (SGC-7901), human non-small cell lung cancer cells (A549) and human HeLa cervical cancer cells, with ICsub.50 values ranging from 3.32 to 60.36 µM, respectively. Compounds 2, 6 and 7 showed potent inhibitory activity against α-glucosidase, with ICsub.50 values of 1.26 ± 0.19, 2.16 ± 0.44 and 13.22 ± 0.55 µM, respectively.