vs Olimar you have to learn to space nair. You have to space it right into Olimar from a full hop or platform drop (from full jump, you should fast-fall it), so it feels like it'll hit no matter which side he moves to. You also have to activate it a bit early so it counters usmash if he does it. Once nair hits, you combo from there (buffergrab/walkgrab/dash attack/usmash: depends).
The tricky part is that you also have to hit him at the side or his back once you're there and drift away from him if he blocks, so he whiffs usmash if he does it and you can then dash attack him, jab to clash with it and then punish or just move away. I think nair is very important as you can guess.
I also think it's best to move onto platforms so pikmin never latch onto you. Shining a white may be pretty good but remember that pitmin toss is the only move in the game you can't hop after reflecting (what's wrong with you sakurai?). Some of the best moves to use if they do is AC full hop dair onto platform, and shine which takes them off in one blow but doesn't work on yellows. Blocking and air-dodging the latched pikmin's hits around can work too LOL...but if it's best to focus on the Oli because he's going for offense, then do that. The only move I've used to get pikmin off of Fox's ears is utilt (shine doesn't reach LOL), but I haven't tried fsmash, usmash, nor sideb (maybe it takes them off quickly :O). Dash away +usmash sounds pretty good for it...
Anyway, use the safe approaches and live in the air. Sneak blasters in when you can (eg when falling from plat since it takes much less time than sh blaster). Having the lead and escaping is a good idea. Olimar's a slow char.
As for Oli chasing you at the air, dair trades with 2 hits of Oli's uair so it's easy for it to counter it, and air-dodging (with fast-fall if you can) when you think the opponent will hop to try to catch you is great: Oli will be above you or stuck in an aerial's animation which is bad for him. Dair beats his usmash too btw, but it's easy for him to block+usmash so be aware of that.
To juggle Oli, watch out for his aerials, try to block and punish them, or bait them (so you can dash attack a whiffed aerial or an air-dodge). If you get directly below Oli, tipper utilt from below works like it does vs most chars. Walk up block works to shield-grab many of his landings too.
CP stages I recommend are Stadium 2, Stadium, and Battlefield, in that order. Lylat is good too because of the platforms: low and numerous for easy approaching. Illusion cancel level 3 from one side of the stage to a platform on the other is something Olimar simply can't catch up to. Full jump + airjump fair + shines are great for making time, and the level 3 illusion if you need it or is a free escape is icing on the cake.
That's why it's best to avoid the pikmin latches: for the advantage in damage, so you can pressure the opponent with the timer.