I am relatively new to poker so pardon me if this question is a bit too basic for this forum.

I'm not very familiar with calculating when you are getting good odds to call a hand or fold. Yesterday, this hand came up while playing 1/2 NL live at a casino, and after I folded my cards, someone setting next to me (he saw my cards) mentioned that I was getting the correct odds for calling and should have called.

I was in the Small Blind position ($305 stack) with 44. The pot was limped around and it went 6-handed to the flop.

J43

I bet $20 and got 2 callers. Both players had position on me and both had more chips than me. Turn was a 6

I bet $70. The person acting after me raised it to $200. Next person went all in for ~350. It came around to me and I folded. I put atleast one person on 75 or 25 or 66 since it was a limped pot.

River was 6. So board reads J4366

Initial raiser flipped 75. All in person had 33 and won the pot.

Was I getting the correct odds for calling even though I was behind on the turn?

I think this is a reasonable enough question for this forum.

If you are absolutely sure someone has a straight, and not a set of jacks (because you have 1 out only to beat JJJ), then you can win with any J, 4, 3 or 6. There are 3 Js, 1 4s, 3 3s, and 3 6s, a total of 10 outs for a full house. There are 44 unknown cards (we know our 2, we know 4 on the board, and we "know" that a 7 and 5 are out, so we know 8 cards). So, your chance of getting there is 10/44 or 3.4:1

A 6-handed limp would have $12 or so in the pot. You bet $20 on the flop and got 2 callers so that's $60 more. You bet $70 on the turn, so your stack would have about $305-$20-$70=215 to call.
$12+$60+$70+$270+$270=$682
(assuming that the guy who bet $200 had $70 more and would call)
So your pot odds are $682 : $215 = 3.17:1

This is a bit worse than the odds you'd need if I did the numbers right, but it's close enough to call. Of course, if you knew that the other guy had 33 then you have 2 less outs and it's probably closer to a fold.

Er, 3 less outs: the two 3s in the other guy's hand, and the last 3 in the deck, since then you lose to quads!

Good point.

It could go either way. A call or fold isn't bad in this situation, it sounds like you had the proper reads. No one would've beat up on you for calling or folding here.

You should definitely pickup some reading material on poker math, it's an absolute fundamental.