Dictionary.com has a definition for clunk as follows:
4. Informal. a stupid person; clunkhead.
However, as FumbleFingers remarks in a comment to the question, it is a rare epithet. Searching for "we were clunks", the mighty engine can tell me in 0.17 seconds that the result is unique in cyberspace. Out of the 46 results given for "we were both clunks", 44 of them are direct quotations of that book, and the first and second results link to this question.
I'm not sure of the etymology of this phrase, but I can say something about its meaning and connotations.
"Regular old" means something more along the lines of "a typical" (or even "stereotypical" though in the sense of "expected", not in the negative sense that "stereotypical" often connotes). In other words, something basic and ordinary, but not unusual in any respect. It has a soft, congenial connotation of simplicity and straightforwardness, definitely not fancy or elaborate. And this interpretation works for all the examples you've listed.
So in the first example, the author is referring to typical examples of programmatic features for an object oriented language.
In the second example, the A chord could be viewed as the most basic and simple of chords around which all others are mere adornments.
In the third example, I would assume it's much the same but I feel I'd need more context to understand what "she" meant by "image". And, I'm not familiar with the word "crawler" either.
In the fourth example, this is a feast as you would expect a feast to be.
In the fifth example, the woman isn't downplaying herself. She's just saying she's not complicated, she's not one to create drama for others. She's your basic congenial old lady. If there's any negative connotation here, it's not created by the use of the phrase "regular old". Rather it's created by the following sentence in which she describes her daily life as "boring".
In the last example, the implication is that, since these house are not "regular old" ones, they are quite lavish, which is supported by the following sentence.
Best Answer
I'm not familiar with the term, and I can find no obvious definition online. But one can find a few uses of the term, and enough cases where "Ninny-Pinny" is used as a user ID to suggest that it's familiar to some group of people.
Some of the uses:
1 Ah, to be able to bring a pause to this whole mess, to the ninny-pinny men giving useless advice, to the bad news (to the endless briefings on the state of the economy and the ever-worstening crime in the streets).
2 "O Jo! how can you be such a ninny-pinny?"
(It should be noted that the above appears to be a quote from Alcott's Little Women, though I cannot locate the corresponding passage in the Google Books copy.)
3 At times, I feel a desperate need to write, but I fear that what I want to write most is from personal experience. Things that may scrape so close to the bone as to be painful to those I know and love and have no desire to wound. (And YES, I know that last sentence was a fragment, brain. Stop being a ninny pinny.) (Oh, for goodness' sake, now I'm looking up ninny pinny. I give up on me.)
The evidence suggests that the term is basically a sort of "rhyming slang" version of "ninny", which has already been defined above as a "foolish or stupid person". Very likely the appearance in Alcott's book (if indeed it did) gave what would have been a nonce term "legs" among the audience of Alcott's admirers.