Alzheimer’s disease (AD), a multifactorial neurodegenerative disorder characterized by severe cognitive impairment, affects millions of people worldwide. However, AD therapy remains limited and mainly symptomatic-focused, with acetylcholinesterase (AChE) inhibitors being the major available drugs. Thus, AD is considered by the WHO as a disorder of public health priority. Among several strategies that have been identified to combat AD, the use of natural multi-target drug ligands (MTDLs) appears to be a promising approach. In this context, we previously found that the essential oils (EOs), obtained via hydrodistillation, from Azorean Cryptomeria japonica sawdust (CJS) and resin-rich bark (CJRRB) were able to exert antioxidant activity via different mechanisms of action. Therefore, in the present work, these EOs were screened for their (i) in vitro anti-AChE and anti-butyrylcholinesterase (BChE) activities, evaluated by a modified Ellman’s assay; (ii) in vitro anti-inflammatory potential, using the albumin denaturation method; and (iii) toxicity against Artemia salina. The CJRRB–EO exhibited both anti-AChE and anti-BChE activities (IC50: 1935 and 600 µg/mL, respectively), whereas the CJS–EO only displayed anti-BChE activity, but it was 3.77-fold higher than that of the CJRRB–EO. Molecular docking suggested that α-pinene and ferruginol compounds contributed to the anti-AChE and anti-BChE activities, respectively. Moreover, the anti-inflammatory activity of the CJS–EO, the CJRRB–EO, and diclofenac was 51%, 70%, and 59% (at a concentration of only 2.21 μg/mL), respectively, with the latter two presenting comparable activity. Concerning the EOs’ potential toxicity, the CJRRB–EO exhibited a lower effect than the CJS–EO (LC50: 313 and 73 µg/mL, respectively). Overall, the EOs from C. japonica biomass residues, chiefly the CJRRB–EO, displayed antioxidant, anticholinesterase, and anti-inflammatory activities in a concentration-dependent manner. These properties demonstrate that these residues may be suitable natural MTDLs for AD complementary therapy when administered through aromatherapy, or, alternatively, could serve as low-cost sources of valuable ingredients, such as α-pinene.