Asexual rhymes with:
annual, continual, emanuel, emmanuel, manual, transsexual, annual, audiovisual, biannual, bisexual, conceptual, consensual, continual, contractual, emanuel, emmanuel, eventual, factual, gradual, habitual, ineffectual, intellectual, manual, massmutual, menstrual, parimutuel, pascual, perpetual, punctual, residual, ritual, sexual, transsexual, virtual
Asexual sounds like:
accel, accola, achille, ackley, acocella, agile, aglo, aglow, agoglia, aguila, aguilo, aichele, aisle, akali, akel, akella, aquila, ashley, ashwell, asiel, assail, asshole, augello, ausley, axel, axial, axle, axley, azalea, azalia, azelia