  We investigate the helium dimer in strong magnetic fields, focusing on the
spectrum of low-lying electronic states and their dissociation curves, at the
full configuration-interaction level of theory. To address the loss of
cylindrical symmetry and angular momentum as a good quantum number for
nontrivial angles between the bond axis and magnetic field, we introduce the
almost quantized angular momentum (AQAM) and show that it provides useful
information about states in arbitrary orientations. In general, strong magnetic
fields dramatically rearrange the spectrum, with the orbital Zeeman effect
bringing down states of higher angular momentum below the states with pure
$\sigma$ character as the field strength increases. In addition, the spin
Zeeman effect pushes triplet states below the lowest singlet; in particular, a
field of one atomic unit is strong enough to push a quintet state below the
triplets. In general, the angle between the bond axis and the magnetic field
also continuously modulates the degree of $\sigma$, $\pi$, and $\delta$
character of bonds and the previously identified perpendicular paramagnetic
bonding mechanism is found to be common among excited states. Electronic states
with preferred skew field orientations are identified and rationalized in terms
of permanent and induced electronic currents.
