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We present two kinds of resonance soliton solutions on the Ultrahyperbolic space $\mathbb{U}$ for the G=U(2) Yang equation which is equivalent to the anti-self-dual Yang-Mills (ASDYM) equation. We reveal and illustrate the solitonic behaviors in four-dimensional Wess-Zumino-Witten (WZW$_4$) model through the sigma model action densities. The WZW$_4$ model on $\mathbb{U}$ describes a string field theory action of open N=2 string theories and hence our solutions suggest the existence of the corresponding classical objects in the N=2 string theories. Our solutions include multiple-pole solutions and V-shape soliton solutions. The V-shape solitons suggest annihilation and creation process of two solitons and would be building blocks to classify the ASDYM solitons, like the role of Y-shape solitons in classification of the KP (line) solitons. We also clarify the relationship between the Cauchy matrix approach and the binary Darboux transformation in terms of quasideterminants. Our formalism can start with a simpler input data for the soliton solutions and hence might give a suitable framework of the classification of the ASDYM solitons., Comment: 35 pages, 16 figures