We propose a Clifford algebra based model, which includes local gauge symmetries SO(1,3)*SU_L(2)*U_R(1)*U(1)*SU(3). There are two sectors of bosonic fields as electroweak and Majorana bosons. The electroweak boson sector is composed of scalar Higgs, pseudoscalar Higgs, and antisymmetric tensor components. The Majorana boson sector is responsible for flavor mixing and neutrino Majorana masses. The LHC 750 GeV diphoton resonance is identified as a Majorana sector quadruon, which is the pseudo-Nambu-Goldstone boson of $\bar{u}_Rs_R\bar{c}_Rd_R$ four-quark condensation. The quadruon results from spontaneous symmetry breaking of a flavor-related global U(1) symmetry involving right-handed up, down, charm, and strange quarks. In addition to $\bar{u}_Rs_R\bar{c}_Rd_R$, four-fermion condensations can also involve three other right-handed configurations $\bar{u}_R\tau_R\bar{\nu}_{\tau R}d_R$, $\bar{c}_R\mu_R\bar{\nu}_{\mu R}s_R$, and $\bar{\nu}_{\mu R}\tau_R\bar{\nu}_{\tau R}\mu_R$. Free from gauge interactions, these four-fermion condensations are potential dark matter candidates.