Do the Androids have ki or another source of energy? If so does, Android 16 have ki since he is fully mechanical and only living beings have ki?
I'd like to believe she has Ki, because she is part human. At the world tournament Goku asks how her and Krillin had a child together and he explains that she was human to begin with and turned into an android by Dr. Gero. (Season 7 episode 208 or 209)(I can't remember exactly)
"The correct term is Cyborg. Human with cybernetic parts, she was human by birth and turned into a cyborg, thus retaining certain human functionality, such as being able to get pregnant."
But that still raises the question why Goku and the others couldn't detect their energy. I guess some things should just be left unasked?
Though I have to look it back up, a major thing is that their source of power was physical generators in their bodies. I recall there were even claims that they had unlimited power thanks to these generators. This is likely the source of their actual power.
As for why they are undetectable, there is a simple but fairly theoretical explanation for that. Scouters and the Z warriors general ability to sense power is not full proof, and in fact they work about the same. The Z warriors specifically learned how to suppress their power, which throws the sensing methods off, even to a point where scouters could not detect Gohan and Krillin on Namek. In a way, you could say they are leaking power, and that leaking of power is what is detectable. By actively containing it, it can't be detected. Androids have a purely mechanical method of generating power. It is completely feasible that because it is mechanical, instead of biological, it does not leak power, hence there is no surplus of power around them to detect.
In that way, all the androids do have some kind of Ki (as it can be used in the same way as Ki), and is undetectable for the same reason that Scouters were ineffective against the Z warriors on Namek.
Just watched the first few episodes of Dragon Ball Z Kai with the androids yesterday: they say that the living people like Goku and Vegeta can't detect any ki from the androids (also see http://dragonball.wikia.com/wiki/Android_19), and that includes both 19 and 20 who absorb ki from people (although anime says "energy" never "ki"). Also, 20 has Dr. Gero's brain, so some part of him is alive I guess, but also isn't detected as ki when people are searching for him in the rocky hills after 19 is defeated. So, must not be ki.
16 does not have ki, hence he uses laser eyes and arm cannons. 17 and 18 do, that is why they are able to use ki blasts. Just look at how 18 learned destructo disc. It's really simple, they use the suppression technique so the Z Warriors wouldn't sense them.