Performance assessment and optimization for networks jointly performing caching, computing, and communication (3C) has recently drawn significant attention because many emerging applications require 3C functionality. However, studies in the literature mostly focus on the particular algorithms and setups of such networks, while the theoretical understanding and characterization of such networks has been less explored. To fill this gap, this paper conducts the asymptotic (scaling-law) analysis for the delay-outage tradeoff of noise-limited wireless edge networks with joint 3C. In particular, we derive closed-form expressions for the optimum outage probability as function of delay and other network parameters via first obtaining the outage probability expression and then deriving the optimal caching policy. We provide insights and interpretations based on the derived expressions. Computer simulations validate our analytical results and insights.