Step-by-step analysis:

1. Analyze the structures and electronic effects in each compound:

   • Compound I (Aniline, $C_6H_5NH_2$): This is a primary aromatic amine. The lone pair of electrons on the nitrogen atom is delocalized into the benzene ring through resonance (-R effect). This delocalization decreases the electron density on the nitrogen, making it a weak base. The phenyl group also exerts an electron-withdrawing inductive effect (-I effect).
   • Compound II (Cyclohexylamine, $C_6H_{11}NH_2$): This is a primary aliphatic amine. The lone pair on the nitrogen is localized as there is no resonance. The cyclohexyl group is an alkyl group and exerts an electron-donating inductive effect (+I effect), which increases the electron density on the nitrogen. Thus, it is a strong base.
   • Compound III (N,N-dimethylaniline, $C_6H_5N(CH_3)_2$): This is a tertiary aromatic amine. Similar to aniline, the lone pair on nitrogen is delocalized into the benzene ring (-R effect), making it a weak base. The two methyl groups have a +I effect, which increases the electron density on nitrogen compared to aniline. Therefore, N,N-dimethylaniline is slightly more basic than aniline.
   • Compound IV (N,N-dimethyl-2,6-dimethylaniline): This is a tertiary aromatic amine with two methyl groups at the ortho positions. These bulky ortho groups cause steric hindrance with the methyl groups on the nitrogen. This steric strain forces the $-N(CH_3)_2$ group to rotate out of the plane of the benzene ring. This phenomenon is called Steric Inhibition of Resonance (SIR). As a result, the delocalization of the nitrogen's lone pair into the ring is prevented. The lone pair becomes localized on the nitrogen atom, making it highly available for protonation. This makes compound IV a very strong base, comparable to aliphatic amines.

2. Evaluate each statement:

   • A: The order of basicity is II > I > III > IV.

     • Based on our analysis, the basicity depends on the availability of the lone pair.
     • IV is a very strong base due to the SIR effect, which localizes the lone pair.
     • II is a strong base because it's an aliphatic amine with a +I group and no resonance.
     • III is a weak base due to resonance, but stronger than I due to the +I effect of two methyl groups.
     • I is a weak base due to resonance.
     • The approximate pKb values are: I($\approx 9.4$), II($\approx 3.4$), III($\approx 8.9$), IV($\approx 2.9$). A lower pKb value indicates a stronger base.
     • The correct order of basicity is IV > II > III > I.
     • Therefore, statement A is incorrect.

   • B: The magnitude of pKb difference between I and II is more than that between III and IV.

     • Let's calculate the differences using the pKb values.
     • Magnitude of pKb difference between I and II: $|\Delta pK_{b (I, II)}| = |pK_b(I) - pK_b(II)| \approx |9.4 - 3.4| = 6.0$.
     • Magnitude of pKb difference between III and IV: $|\Delta pK_{b (III, IV)}| = |pK_b(III) - pK_b(IV)| \approx |8.9 - 2.9| = 6.0$.
     • Using more precise literature values: $pK_b(I) = 9.37$, $pK_b(II) = 3.34$, $pK_b(III) = 8.85$, $pK_b(IV) = 2.80$.
     • $|\Delta pK_{b (I, II)}| = |9.37 - 3.34| = 6.03$.
     • $|\Delta pK_{b (III, IV)}| = |8.85 - 2.80| = 6.05$.
     • The values are nearly identical, with the difference between III and IV being slightly larger. Thus, the statement that the difference between I and II is more than that between III and IV is incorrect.

   • C: Resonance effect is more in III than in IV.

     • In compound III, the lone pair on the nitrogen atom can effectively delocalize into the benzene ring, as the $-N(CH_3)_2$ group can adopt a conformation that is nearly coplanar with the ring.
     • In compound IV, due to the steric hindrance from the ortho-methyl groups (SIR effect), the $-N(CH_3)_2$ group is twisted out of the plane of the ring. This prevents effective overlap between the nitrogen's p-orbital and the ring's $\pi$-system, thereby inhibiting resonance.
     • Therefore, the resonance effect is significantly greater in III than in IV.
     • This statement is correct.

   • D: Steric effect makes compound IV more basic than III.

     • The basicity of an amine is determined by the availability of its lone pair. In compound III, the lone pair is delocalized by resonance, making it less available and thus less basic.
     • In compound IV, the steric hindrance (SIR effect) prevents this resonance. The lone pair is localized on the nitrogen atom, making it much more available for protonation. This results in a dramatic increase in basicity.
     • Therefore, the steric effect is directly responsible for making compound IV much more basic than compound III.
     • This statement is correct.

Final Conclusion:

Statements C and D are the correct statements.