Dad has 34 years and Mom, will have the 40 years by 65He definitely should claim his OAS immediately. It is also retroactive up to max 11 months prior to application. He should only back date it to the month following his 70th B/day. Provided he has 40 years in Canada before age 65 he will get the max age 65 amount (if he has less years its prorated) plus 36% because he's starting it at 70 so about $870 a month. However OAS does get clawed back when income hits about 80,000 at the rate of 15% so he will have some claw back if his income is 100,000, but he will still get a lot (about 7500 yr) and as his income will likely drop when he retires the claw back amount will also drop. His OAS has nothing to do with your Mum claiming anything, but where possible income should be shifted to her to reduce his income and the clawback and to be income tax efficient. When he starts his work pension up to 50% can be split with her.
I see Dad has made 30 years of CPP contributions so they've been here a while but OAS is based on years in Canada after age 18. How many years in Canada? That info is needed to be more accurate.