In general, you should never take bets on like this with anyone astute. Just as Damon Runyen so rightly quotes:
“One of these days in your travels, a guy is going to show you a brand new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you’re going to wind up with an ear full of cider.”
However, solid chunks of money are lost by players going one handicap too far, so it is always worth thinking about each of these offers before just instantly writing them off.
First up, the offer of the breaks. This is not really an edge, as you can't break and clear, and really, its very hard for them to break anyway. Although its easy enough to hit balls around softly with nearly any object, hitting a ball hard without a cue tip and chalk is very, very difficult. Not much edge here - it's possibly even worth trying to get alternating breaks.
So let's look at the items. Believe it or not, I've won money pool games with all of these objects, but some are significantly harder than others, and having a grasp of what things to think about in an object is critical to evaluating these bets well.
a) Sounds very easy but the weighting is off, the tip is not great and it's a little harder than it might seem. Of all the objects I've seen good players play with, this is the one most over estimate their ability with as it is actually quite different from the right way around. Despite all of this, its still a long object of the right weight. You will most likely be a dog here.
b) A coke bottle is a surprisingly effective object to play with. The tip is decent and flat, you can bridge with it and can stroke relatively straight with it. The big downside is that the bottle is too small, which makes a lot of shots awkward. This is the key leak with this, and it stands alone against the other long objects. If you can play clever safeties to take advantage of this, you have some equity, but in normal play you will still get ripped up.
c) By far the easiest of the three. No weight problems, decent(ish) tip, decent weight, right length. Run a mile.
d) Looks tough as well on the face of it, but actually surprisingly easy. Nice even weight, flat end, ok length, easy(ish) bridging. You won't have much of an edge.
As you can see from the above, you are most likely behind in all cases here, but you are behind by differing amounts. If you can secure some extra weight some of these might close in on +EV.
Solution: In normal situations you should avoid all four, if desperate to at least play a few games, pick the coke bottle and try and take advantage of its shortness.