We study the relation between quasi-normal modes (QNMs) and transmission resonances (TRs) in one-dimensional (1D) disordered systems. We show for the first time that while each maximum in the transmission coefficient is always related to a QNM, the reverse statement is not necessarily correct. There exists an intermediate state, at which only a part of the QNMs are localized and these QNMs provide a resonant transmission. The rest of the solutions of the eigenvalue problem (denoted as strange quasi-modes) are never found in regular open cavities and resonators, and arise exclusively due to random scatterings. Although these strange QNMs belong to a discrete spectrum, they are not localized and not associated with any anomalies in the transmission. The ratio of the number of the normal QNMs to the total number of QNMs is independent of the type of disorder, and slightly deviates from the constant $sqrt{2/5}$ in rather large ranges of the strength of a single scattering and the length of the random sample.
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