The fine structure of multi-compartment neurons captures both temporal and spatial characteristics, offering rich responses and intrinsic mechanisms. However, current studies on the effects of channel blocking and noise on neuronal response states are predominantly limited to single-compartment neurons. This study introduces an analytical method to explore the internal mechanisms of channel blocking and noise effects on the response states of multi-compartment neurons, using the smooth Pinsky-Rinzel two-compartment neuron model as a case study. Potassium, sodium, and calcium ion channel blocking coefficients were separately introduced to develop a smooth Pinsky-Rinzel neuron model with ion channel blocking. Methods such as single-parameter bifurcation analysis, double-parameter bifurcation analysis, coefficient of variation, and frequency characteristics analysis were employed to examine the effects of various ion channel blockings on neuronal response states. Additionally, smooth Pinsky-Rinzel neuron subunit noise models and Conductance noise models were constructed to investigate their response characteristics using interspike interval analysis and coefficient of variation indicators. Subthreshold stimulation was used to explore the presence of stochastic resonance phenomena. Single-parameter bifurcation analysis of the ion channel blocking model elucidated the dynamic processes of two torus bifurcations and limit point bifurcations in Pinsky-Rinzel neuron firing under potassium ion blocking. Double-parameter bifurcation analysis revealed a near-linear increase in the Hopf bifurcation node of potassium ions with input current, whereas sodium ions exhibited a two-stage pattern of linear decline followed by exponential rise. Analysis of average firing frequency and coefficient of variation indicated that moderate potassium channel blocking promoted firing, sodium channel blocking inhibited firing, and calcium channel blocking showed complex characteristics but primarily promoted firing. Subthreshold stimulation of the channel noise model demonstrated stochastic resonance phenomena in both models, accompanied by more intense chaotic firing, highlighting the positive role of noise in neural signal transmission. Interspike interval and coefficient of variation indicators showed consistent variation levels for both noise models, with the conductance model displaying greater sensitivity to membrane area and stronger encoding capabilities. This study analyzed the general frequency characteristics of potassium and sodium ions on a multi-compartment neuron model through ion channel blocking models, providing particular insights into the unique effects of calcium ions. Further, the study explored stochastic resonance using ion channel noise models, supporting the theory of noise-enhanced signal processing and offering new perspectives and tools for future research on complex information encoding in neural systems. By constructing ion channel blocking models, the research analyzed the effects of potassium and sodium ions on the frequency characteristics of multi-compartment neurons and revealed the special influences of calcium ions. Using ion channel noise models, the study investigated stochastic resonance, supporting the theory that noise enhances signal processing. This research offers new perspectives and tools for studying complex information encoding in neural systems.