I think the main point of confusion lies with the wording of the Swift Aid feat. While it says:
As a swift action, you can attempt the aid another action
it then immediately follows that with new rules that contradict it
granting your ally...a +1 bonus
I take that as a replacement for the basic +2 bonus for aiding another, not in addition to it. My rule of thumb is that specific cases override general ones. Aid Allies replaces the bonus for all uses of the aid another action, and Swift Aid only replaces the bonus when aiding another as a swift action; so if I were forced to play by rules as written, I would give Swift Aid the final word, and the beneficiary would receive a +1.
Looking at it from the perspective of rules as intended however, it's obvious that Swift Aid was meant as a reduced benefit for a reduced cost, but I see no reason why the two abilities should not work together. Going by the same logic as above, I would still apply Aid Allies first, then Swift Aid. That then leaves the GM to decide how far to reduce the Swift Aid bonus (with the simplest options being a -1 penalty to the bonus, or a x1/2 penalty to the bonus).
Best Answer
Swift Aid grants a lesser bonus than the normal aid another action
The bonus granted by the feat Swift Aid is correct: the feat's benefit does, in fact, only grant "your ally either a +1 bonus on his next attack roll or a +1 bonus to his AC" instead of the normal +2 bonus granted by the aid another action.
Ask the GM if your own aid another actions stack
The GM must determine if the same creature can use aid another on an ally multiple times and in the same area (like the ally's AC or attack roll). The text of aid another only says, "Multiple characters can aid the same friend, and similar bonuses stack," and is silent on whether one character can aid the same friend multiple times. You'll have to ask the GM how this works. I'm certain a creature with the feat Swift Aid can, in one turn, aid two different allies, but it's up to the GM whether the creature can aid the same ally twice in different areas or if the ally can aid the same ally twice in the same area.
This GM would likely allow a PC that wanted to spend actions aiding another to do so if that's how the player wanted to have fun, but this GM would also likely nix recruiting a band of halfling investigators that've all taken the investigator talent effortless aid and the trait Helpful.
The answer should be Yes, but politeness demands asking the GM anyway if aid allies can be combined with Swift Aid
The cavalier order Order of the Dragon extraordinary ability aid allies says
Because the special ability aid allies doesn't care how the cavalier is aiding another, its benefit should replace the normal benefit of the feat Swift Aid. However, once again, as it's potentially abusive to recruit a platoon of helpful halfling cavalier/investigators to follow around a PC, the GM should be warned ahead of time about this interaction.