Depending on how many Autumn Olive you are cutting, you may also want to look at Pathway. It is essentially the same chemical as Tordon rtu, but in a 2 1/2 gallon jug. You can get it about 30% cheaper by buying the large quantity. I prefer Tordon rtu or Pathway to concentrated Glyphosate products, because on some species, the glyphosate will suppress the stump sprouts for 2-3 years and then all the sudden you find some re-growth. That is my personal preference though.
I always use a spray bottle to apply herbicide to cut stumps. I feel the Tordon rtu bottle is a little too liberal with the spray. I have always gotten along fine with the sprayer so have not tried any other methods. wildbio is right on about following label directions. Tordon rtu is notorious about moving through the soil and causing residual damage if you over apply. It can lead to a big bare spot on the ground.
As for sericea, wildbio is right on again. One additional thing to consider is to burn off the field/s with the sericea problem in April. That will stimulate additional sericea seeds to germinate. You will still have to hit it every year, but you can get rid of much of the seedbank by burning first. When spot treating sericea, it is easiest in June because at that time, it tends to be about the tallest plant in the field. If it gets to the flower stage before you get to it, you can hit it with Ally or Escort and still kill it. Even if you have to mow a patch of sericea in September because you can't get to it yet with chemical, do what you can to prevent it going to seed. Then make sure to hit it the next June.
Dealing with invasives is a real pain and we will be dealing with them for as long as we manage wildlife. Good luck and if you need more advice, hit up your local PLC.
Note: MDC (therefore me) does not recommend any one chemical over another. The brand names I used are herbicides I've used and am familiar with. There are other effective herbicides available and feel free to shop around.