To improve the modeling resilience of silicon strong physical unclonable functions (PUFs), in particular, the APUFs, that yield a very large number of challenge response pairs (CRPs), a number of composited APUF variants such as XOR-APUF, interpose-PUF (iPUF), feed-forward APUF (FF-APUF),and OAX-APUF have been devised. When examining their security in terms of modeling resilience, utilizing multiple information sources such as power side channel information (SCI) or/and reliability SCI given a challenge is under-explored, which poses a challenge to their supposed modeling resilience in practice. Building upon multi-label/head deep learning model architecture,this work proposes Multi-Label Multi-Side-channel-information enabled deep learning Attacks (MLMSA) to thoroughly evaluate the modeling resilience of aforementioned APUF variants. Despite its simplicity, MLMSA can successfully break large-scaled APUF variants, which has not previously been achieved. More precisely, the MLMSA breaks 128-stage 30-XOR-APUF, (9, 9)- and (2, 18)-iPUFs, and (2, 2, 30)-OAX-APUF when CRPs, power SCI and reliability SCI are concurrently used. It breaks 128-stage 12-XOR-APUF and (2, 2, 9)-OAX-APUF even when only the easy-to-obtain reliability SCI and CRPs are exploited. The 128-stage six-loop FF-APUF and one-loop 20-XOR-FF-APUF can be broken by simultaneously using reliability SCI and CRPs. All these attacks are normally completed within an hour with a standard personalcomputer. Therefore, MLMSA is a useful technique for evaluating other existing or any emerging strong PUF designs.