Step 1: Analyze each statement/combination in the table.
\begin{itemize}
\item I. Excitatory Post Synaptic Potential (EPSP):
\begin{itemize}
\item Neuronal event: Excitatory Post Synaptic Potential (EPSP)
\item Ion movement: EPSPs are caused by the influx of positive ions, primarily Na$^+$ (sodium ions), into the postsynaptic neuron.
\item Effect on neuron: The influx of positive ions makes the inside of the cell less negative, leading to depolarization (a shift towards a more positive membrane potential), which brings the neuron closer to its firing threshold.
\end{itemize}
This statement is Correct.
\item II. Inhibitory Post Synaptic Potential (IPSP):
\begin{itemize}
\item Neuronal event: Inhibitory Post Synaptic Potential (IPSP)
\item Ion movement: IPSPs are typically caused by the influx of Cl$^-$ (chloride ions) or the efflux of K$^+$ (potassium ions) from the postsynaptic neuron. Both make the inside of the cell more negative.
\item Effect on neuron: The effect of IPSP is hyperpolarization (making the membrane potential more negative) or stabilization of the membrane potential, making it harder for the neuron to reach its firing threshold. The table states "Depolarisation," which is incorrect for IPSP.
\end{itemize}
This statement is Incorrect.
\item III. Action Potential:
\begin{itemize}
\item Neuronal event: Action Potential
\item Ion movement: The rising phase (depolarization) of an action potential is characterized by a rapid influx of Na$^+$ (sodium ions) through voltage-gated sodium channels.
\item Effect on neuron: This rapid influx causes a sharp, transient change in membrane potential, creating a "spike" or nerve impulse.
\end{itemize}
This statement is Correct.
\item IV. Threshold stimulus:
\begin{itemize}
\item Neuronal event: Threshold stimulus
\item Ion movement: A threshold stimulus is the minimum level of stimulation required to initiate an action potential. It causes a sufficient depolarization to open voltage-gated sodium channels. The ion movement associated with \textit{generating} an action potential at threshold is typically Na$^+$ influx, not Cl$^-$ influx. Cl$^-$ influx is usually associated with inhibition (IPSPs).
\item Effect on neuron: A threshold stimulus indeed leads to the generation of an action potential. However, the associated ion movement (Cl$^-$ influx) is incorrect.
\end{itemize}
This statement is Incorrect.
\end{itemize}
Step 2: Identify the correct combinations from the analysis.
Based on the analysis:
\begin{itemize}
\item Statement I is Correct.
\item Statement II is Incorrect.
\item Statement III is Correct.
\item Statement IV is Incorrect.
\end{itemize}
Therefore, the correct combinations are I and III.
Step 3: Conclude the correct option.
The option that lists I and III as correct is the answer.
The final answer is $\boxed{\text{I and III}}$.