A considerable number of higher-angular-momentum states of the helium atom embedded in a magnetic field B=0-100 a.u. are investigated using a full configuration-interaction approach which is based on a nonlinearly optimized anisotropic Gaussian basis set of one-particle functions. Spin singlet and triplet states with positive- and negative-z parity are considered for the magnetic quantum number M=+/-2 and positive-z parity states are studied for M=+/-3. Many of the excitations within these symmetries are investigated here. Total energies, ionization energies, as well as transition wavelengths as a function of the field strength are given. A list of stationarities with respect to the field strength which are of immediate interest to astrophysical applications is available.