Structural chromosome rearrangements involving translocations, fusions and fissions lead to evolutionary variation between species and potentially reproductive isolation and variation in gene expression. While the wheats (Triticeae, Poaceae) and oats (Aveneae) all maintain a basic chromosome number of x=7, genomes of oats show frequent intergenomic translocations, in contrast to wheats where these translocations are relatively rare. We aimed to show genome structural diversity and genome relationships in tetraploid, hexaploid and octoploid Avena species and amphiploids, establishing patterns of intergenomic translocations across different oat taxa using fluorescence in situ hybridization (FISH) with four well-characterized repetitive DNA sequences: pAs120, AF226603, Ast-R171 and Ast-T116. In A. agadiriana (2n=4x=28), the selected probes hybridized to all chromosomes indicating that this species originated from one (autotetraploid) or closely related ancestors with the same genomes. Hexaploid amphiploids were confirmed as having the genomic composition AACCDD, while octoploid amphiploids showed three different genome compositions: AACCCCDD, AAAACCDD or AABBCCDD. The A, B, C, and D genomes of oats differ significantly in their involvement in non-centromeric, intercalary translocations. There was a predominance of distal intergenomic translocations from the C- into the D-genome chromosomes. Translocations from A- to C-, or D- to C-genome chromosomes were less frequent, proving that at least some of the translocations in oat polyploids are non-reciprocal. Rare translocations from A- to D-, D- to A- and C- to B-genome chromosomes were also visualized. The fundamental research has implications for exploiting genomic biodiversity in oat breeding through introgression from wild species potentially with contrasting chromosomal structures and hence deleterious segmental duplications or large deletions in amphiploid parental lines.