[UmaroVI]

Edge for Logic: not really.

Edge for Codeslinger: that is a reasonable move, especially since you can buy more Edge later, but you can't buy Codeslinger later.

Multitasking is terrible crap. It was almost a good ability, but it doesn't work during combat, which is the only time you care about how many free actions you get in the first place.

Dermal Sheathing is overpriced and not nearly as useful as Encephalon. Given that you probably don't want to lose any more essence, I would instead plan to save up for higher-grade ware. Alphaware Encephalon is .6, you could then get Alphaware Muscle Toner 4.

[Tecumseh]

In my experience Edge is largely a matter of personal preference. Some players swear by it and max it out, noting (correctly) that its power scales exponentially instead of linearly. Others employ it only as a last resort, keeping a couple points on hand for a particularly critical roll or to stave off certain death. You might want to consult with your GM about how often he/she expects Edge to come up during play. The threat level of the campaign and its margin for error will help answer that question.

If you can't make a decision based on dice, don't be afraid to consult your character concept either. Is your ork just an average Joe (Logic 3) who wanted to get ahead (pun) with the Encephalon and PuSHeD, or was he already brighter-than-average (Logic 4) to begin with and knew that it would pay to be even smarter? Does he have average luck (Edge 3) or does he get an extra share of lucky breaks (Edge 4)?

As for Codeslinger, whether or not you can buy it after character creation is subject to GM discretion. I don't see it as a genetic quality so, personally, I would allow it to be a karma purchase in my game.

I would echo Umaro's suggestions on your cyber/bioware.