Granted, I haven't played any good Ness players offline, but since I play this match-up with my brother a lot (for the past 8 months lolol), I think I know his capabilities pretty well.
Ness' FAir is easily his most annoying aerial; it has a deceptively large hitbox, hits 5 times, and can be auto-canceled from a short-hop. You can out-range it with your FAir, but the spacing has to be pretty tight in order to do so. You can also SDI out of the FAir, which negates it's usefulness, but the point of FAir is to interrupt you and set up for other stuff. His BAir is a great killing move, along with his UAir, and NAir is excellent out of shield. DAir is the second most powerful spike in the game (at low %s before Ganondorf's DAir has the chance to get stronger, it is the most powerful spike in the game) and even if it doesn't spike the non-sweetspot hit is pretty powerful, so watch out for that too.
On the ground, he'll probably be focusing on dash attack to set up for juggles, DThrow to set you up for juggles, and DTilt to get you away. He's not much of a threat here until at high percents (125-ish%) where he'll most likely go for the pummel -> BThrow, which WILL kill you if you don't DI properly (aim for the corner, not straight up) and momentum cancel with DAir + fastfall.
Ike's FAir will cut right through all of Ness' usual attacks save for PK Fire. Don't NAir much, otherwise you'll get out-ranged by his FAir. If he ever shields your jabs, watch out if you go for the grab, since he'll probably use NAir out of shield.
In one of his videos against his brother, metroid tried a reverse Aether but I wouldn't really recommend it as you could mess up and QD to your death, get hit by PKT2, or get edgehogged if you mistime it. This is my opinion though.
Reverse Aetherspiking is pretty risky, but if you practice it you shouldn't have to be afraid of QD'ing to your death (I freely admit that I've done this before
) and if you watch where the Ness aims his PK Thunder, you shouldn't have that much of a problem hitting him with reverse Aether (otherwise you'll get edgehogged... and that always looks stupid). If he's coming from far away (1/2 PKT2 distance), Counter is a great edgeguard, since it'll do a hefty amount of damage and a lot of knockback. A little closer than that, reverse Aether'ing is probably the best option, since you can hit with it from below the stage and above it. You can also BAir him during it if you're close enough during start-up (when he's trying to hit himself) or spike him even, but watch out for the tail portion hitting you. DAir CAN hit him even when he's in PKT2, but not right after he hits himself (during which he has invincibility frames, which is why you can't Counter his recovery 100% of the time). Edgeguarding Ness is probably the most fun part about the match-up, there are just so many ways you can do it.
If you want some laughs, you can always purposely get hit by PKT2 to shorten it's length, then tech against the stage to survive while they fall to their death.
Ike can be edgeguarded like crazy by Ness, however; PK Fire -> DAir spike is a very dangerous combo, especially since Aether cannot auto-sweetspot. If you do get hit by the PK Fire, try to SDI up on the initial hit to break out. You can try to tech the DAir spike if you're close enough to the stage, but that probably isn't going to work.
It could be my bias from playing/beating my brother so often, but it seems as though this match-up is in Ike's favor.