Dual specificity protein kinase activity catalyzing autophosphorylation and phosphorylation of exogenous substrates on both serine/threonine and tyrosine residues (By similarity). Regulates the cellular cytoskeleton by enhancing actin stress fiber formation via phosphorylation of cofilin and by preventing microtubule breakdown via inhibition of TAOK1/MARKK kinase activity (By similarity). Inhibits podocyte motility via regulation of actin cytoskeletal dynamics and phosphorylation of CFL1 (By similarity). Positively regulates integrin- mediated cell spreading, via phosphorylation of cofilin (PubMed:15584898). Suppresses ciliogenesis via multiple pathways; phosphorylation of CFL1, suppression of ciliary vesicle directional trafficking to the ciliary base, and by facilitating YAP1 nuclear localization where it acts as a transcriptional corepressor of the TEAD4 target genes AURKA and PLK1 (PubMed:25849865). Probably plays a central role at and after the meiotic phase of spermatogenesis (By similarity). {ECO:0000250|UniProtKB:O70146, ECO:0000250|UniProtKB:Q63572, ECO:0000269|PubMed:15584898, ECO:0000269|PubMed:25849865}. This is the function of TESK1 (testis associated actin remodelling kinase 1, Ensembl gene identifier ENSG00000107140).