The EPSG Geodetic Parameter Dataset has 6 transformations from Ain el Abd to WGS 1984. All are supported in ArcGIS. The first two have poor accuracy, approximately 44m and 18m and were derived by the US Defense Mapping Agency (now part of NGA). (1) is valid in Bahrain while (2) is valid in Saudi Arabia. EPSG notes that (3) and (4) give similar results and recommends using (3). Both are valid in Kuwait. (5) and (6) are both listed as 1m accuracy. (5) is valid for "Kuwait - onshore north of a line between Al Jahra' and the Kuwait/Iraq/Saudi Arabia border tripoint" while (6) is onshore south. ArcGIS has another transformation for Bahrain that was given to us by a client. Supposedly, its accuracy is better. The name is WGS_1984_To_Ain_el_Abd_1970_MB (it uses the Molodensky-Badekas method).
WGS 1984 has been designed to conform to various ITRF versions. The latest WGS 1984, G1674, is consistent to ITRF08 (2005.0). For official information on whether there's a transformation or not, see ITRF FAQ. In summary, for ITRF90 and an early version of WGS84, there's a published transformation, but not for later realizations.
Note/Disclaimer: I work for Esri and I'm on the subcommitte that maintains the EPSG Dataset.