While there are several horses in this who started life overseas, we'll just deal with the runners who are still based overseas and with overseas trainers.
No better place to start than with Anthony van Dyck. He's by Galileo out of Believe'n'succeed so he's half-Aussie. His most recent win was at Longchamp in the Prix Foy G2 2000m where he beat Stradivarius by a head. He ran in the Hardwicke at Royal Ascot but no luck and before that and was 2nd in the Coronatiion Cup G1. He won the Derby in 2019 and was 2nd in the Irish Derby and has had 16 starts for 6 wins and 6 places. He's already a millionaire and is rated on 121. He has a wide drawn and top weight but Bowman is not likely to panic and will slot him in to a comfortable spot before choosing to go.
Buckhurst is by Australia and is owner by Lloyd Williams and trained by Joseph O'Brien. He was 5th to Tiger Moth in the "Is It 2021 Yet?" at Leopardstown which is a great race to have on your CV. He's mostly race at G3 level and probably prefers good going. Rated on 114 he's had 10 starts for 4 wins and 3 places.
Dashing Willoughby is by Nathaniel out of the Dylan Thomas mare Miss Dashwood. This year he was 4th in the Lonsdale (3200m) and won the Henry II G3 at Sandown also 3200m, so effectively is down in trip for this although he won a Listed over this. He's had 13 starts for 4 wins and 3 places and is rated on 112,
Prince of Arran is no stranger having been here before. He's raced all around the world and would get the frequent flyer prize this year. However his last win was 973+ days ago but he can find himself in the finish although getting harder since he is now 7.
True Self is also 7 and has been here before and he too hasn't won for a while. You have to respect Willie Mulllins's horses both on the flat and over the jumps and True Self has had 11 starts on the flat for 4 wins and 2 places and he might be better over the Melbourne Cup Trip.