Seeing as your board is 13/15 control hate I would to see how you side all that crap in against CS/BS and Gifts without pulling out combo pieces or anything good.
I don't know what 13/15 your seeing. Unless Rack and Ruin and Pyroclasm are new tech vs. control, I see a
maximum of 11. Duress does not come in versus CS, and neither does Tormod's Crypt. Should the graveyard of CS become a problem, then you have lost, and Duress helps dump their fatties if they get a good brainstorm in response. The Gifts mirror may see Tormod's crypt depending on how Gifts dependant they are. Against something like Smemmen's list I would bring them in, but against Brassman Gifts is a dead card because it can play around it.
You are also using tunnel-vision on my sideboard. Just because a card is good in one matchup, doesn't mean it is crap against everything else. Duress, REB and Tormod's Crypt are all good against at least 2 decks. That is why they are in my sideboard rather than tunnel-vision cards like I am now assuming you run.
It's not so much Rod and Chalice in ICBM Oath, but more so the fact that you're backing Rod and Chalice up with one of the better clocks in the format and the ability to match Gifts counter for counter. Gifts had a superior draw engine over ICBM Oath, but ICBM Oath has the tools to make sure that never becomes an issue.
Rod and Chalice are bitches to face against. They can both be played around however, rod being the harder of the two to do so against. In terms of stopping my draw-engine, I have no idea what you are talking about. Using mana-denial to stop me from using TfK? Spare Moxen in hand usually cry out for TfK to dump them. On top of that I bring in Dark Confidant. Two-mana isn't hard to reach in a proper Gifts deck. I go land turn 1, then land turn 2.

Assuming you lost game one and are dropping chalice, I'm not complaining because I won game one. It takes 1 bounce spell to send that Chalice back to useless. Once again, these are all assumptions made on both sides, and we all know it isn't as easy as dropping Null Rod/Chalice turn 1 with me topdecking all lands and bounce spells.
Gunslinga's and Hydra's posts match my experience. The only thing I have to add is that siding out Tinker takes away one of your best trumps to Oath's gameplan. If it resolves before they resolve an Oath you pretty much completely usurps their role for the matchup, making you into the beatdown deck AND the control deck.
Once again, we are all basing things off experience. It's safe to assume that you haven't faced Gifts with Confidant, because he was immediately discarded as a bad idea when I posted him here. That guy is worse for you than Null Rod is for me. Should he resolve, then you had better drop oath that turn.

In regards to tinker. Once again, if I rely on a 1-of spell against a tight matchup, then I'm screwed. Imagine tutoring for tinker, only to find that your opponent has an extra counter in hand than you. That ends up being pretty game-breaking for the oath player. Game one is just a race. Game two they may be in race mode, while I am comfortable sitting back and playing control. This is how I see it. I haven't played against Oath 60000000 times. Maybe I got lucky in most of my matches. I don't know, but in my playtesting it's been
much better without tinker than with it post-board. Facing a bounce-heavy ICBM oath is my dream matchup game 2, because they should all have a fear of tinker.