a few thigs it could be.the easiest thing is to look to see if any wheel weights fell off the rim and if any tires are cupped or(high and low spots) if that checks out then have the front end aligned at a garage.
I have an 05 Odyssey that has a steering wheel shimmy around 70-75. it comes and goes at those speeds. comes on slowly and builds then goes away after about 20-25 min. comes back 30 minutes later??? sometimes is more pronounced when engine is under power. sometimes shimmies at 65 when engine is coasting??? Have changed tires and had them balanced, also had torque converter changed because of grind at 40-45. Any ideas.
Had a major vibration on my odyssey right around 60-70 mph and after hitting the brakes it would clear up for a second then comeback after accelerating again. Resolved this by replacing cv joints, the inner joint had thrown grease all over the under side of my van and was only really noticable after removing and replacing