To reveal genetic diversity for effective resistance to five foliar diseases and toxic aluminum ions, the entire collection of wheat species from the N.I. Vavilov All-Russian Institute of Plant Genetic Resources (VIR) originating from Ethiopia and Eritrea were studied regarding their traits. The collection contains 509 samples of four wheat species (Triticum aestivum—122 samples; T. aethiopicum—340 samples; T. polonicum—6 samples; and T. dicoccum—41 samples). The majority of accessions are new entries of landraces added to the Vavilov collection as a result of the Russian–Ethiopian expedition in 2012. Wheat seedlings were inoculated with causal agents of leaf rust (Pt), powdery mildew (Bgt), Septoria nodorum blotch (SNB), and dark-brown leaf spot blotch (HLB). The types of reaction and disease development were assessed to describe the levels of resistance. All samples of T. aethiopicum were also screened for seedling and adult resistance to Pt, Bgt, and yellow rust (Pst) under field conditions after double inoculation with the corresponding pathogens. To study tolerance to abiotic stress, seedlings were grown in a solution of Al3+ (185 µM, pH 4,0) and in water. The index of root length was used to characterize tolerance. Seedlings belonging to only two accessions out of those studied—k-68236 of T. aethiopicum and k-67397 of T. dicoccum—were resistant to Pt at 20 °C but susceptible at 25 °C. Specific molecular markers closely linked to the five genes for Pt resistance effective against populations of the pathogen from the northwestern region of Russia were not amplified in these two entries after PCR with corresponding primers. Four entries of T. dicoccum—k-18971, k-18975, k-19577, and k-67398—were highly resistant to Bgt. All samples under study were susceptible to HLB and SNB. Under field conditions, 15% of the T. aethiopicum samples were resistant to Pst, both at the seedling and the flag leaf stages, but all were susceptible to the other diseases under study. Among the evaluated samples, 20 entries of T. aestivum, 1 of T. polonicum (k-43765), and 2 of T. dicoccum (k-18971, k-67397) were tolerant to aluminum ions. The identified entries could be valuable sources for the breeding of T. aestivum and other wheats for resistance to biotic and abiotic stresses.