Preflop and Flop is obviously fine.
Turn: Villains line is certainly strange! But let´s take a look at what hands make most sense for villain to take this line. I don't expect someone to c/c this kind of flop with pure air to float pop, especially not if he´s ABC. Given the Kd completes pretty much any draw (QT, diamonds, KT, etc), it´s hard for villain to have air. On the other hand this is a card which is pretty scary and in general hits the flop cbetter better than the caller. So villain should expect you to bet this card pretty frequently when checked to (as a (semi)bluff and also for value). So I think villain is likely to check the top part of his range (strong flushes) and because the Kd hits your perceived range to c/f the bottom of his flop calling range (9x w/o draw, 3rd pairs).
So villains range for c/c flop - lead turn probably mainly consists of mediocre to strong hands (small flushes, straights, two pairs, AJ, QJ, KQ) without a broadway diamond, because he wants to protect these hands. Given he bets fairly small I´d heavily discount small flushes and straights, but it´s not impossible for him to have these hands. Against this range we could argue for just folding the turn! Given you have the Jd and villain can have air occasionally, calling might be still fine though. Without the Jd it´s for sure a fold. Keep in mind when a reg takes a weird/strange line it´s most often for value.
River: I can definitely see why you consider raising as a bluff and I agree that we can´t really call here! Villains range is likely to be capped, because he´s probably not playing a strong flush this way, especially not with this betsizing. Given his sizing and line villains most likely hands are Kx, two pairs and Qx I think. The problem with raising the river is, I think a lot of people level themselves into calling a raise after underbetting the river, because they think they induced a bluff by underbetting. So I would actually like a raise more if he would have bet a lil bigger (50-60%pot). So I´d probably just fold river as played.
That said, another way to bluff here might be to turn your hand into a bluff on the turn. If you agree with the range I gave him for leading the turn, he´s probably not strong enough to call a turn raise and a rivershove and you should have some equity with the Jd.