Actions for strings and $p$-branes moving in octonionic-spacetime backgrounds and endowed with octonionic-valued metrics are constructed. An extensive study of the bosonic octonionic string moving in flat backgrounds, and its quantization, is presented. A thorough discussion follows pertaining whether or not the analysis leading to the $ D = 26$ critical dimension of the ordinary bosonic string is valid in the octonionic case. A remarkable numerical coincidence is found (without invoking supersymmetry) in that the total number of (real) degrees of freedom of $3$ fermion generations (involving massless Weyl fermions in $ 4D$) is $ 16 \times 4 \times 3 = 192$, and which matches the number of $ 8 \times 24 = 192$ real dimensions (degrees of freedom) corresponding to the $24$ transverse octonionic dimensions associated with the octonionic-worldsheet of a bosonic octonionic-string moving in $D = 26$ octonionic dimensions.