I am looking for any info regarding A 360 4-barrel engine for a 74 Dodge Charger, particularly an SE model. What I have come up with so far is that all charger bodies could have been built with a 360 but the SE had a different engine code. What I have been finding is that Both 360 engine codes offered were 4-barrel engines and I believe both were dual exhaust. What were the differences and why did the SE have a different coded engine than the other charger models?

What 360 letter codes in particular are you referring to?
In the 74 parts catalog two 360 4bbl vin engine codes are listed, J and L. The J code is for a California 360 4bbl and the L code is for the 360 4bbl Hi Performance engine. My 74 360 Road Runner is a California car and has the L code Hi Performance 360 so apparently the Hi Performance 4bbl 360 wasn't a 49 states only option.
E56(J) is the engine code (on the data tag) for the California 360 4bbl and E58(L) was the engine code for the 360 4bbl Hi Performance engine. I also did not see in the Model chart where the Charger SE was available with the E58(L) High Performance 360 4bbl. You could get the E57(K) 360 2bbl or the E56(J) California 4bbl. It seems only the Charger (hardtop 23) or the Charger Coupe (Coupe 21) were available with the E58 Hi Performance 360 4bbl.

Yes that is pretty much what I found that the J code engine is all that was available for an SE With a 360 four barrel. Now the J code is still a four barrel engine did it have dual exhaust?

You'd probably have to look at the build sheet. In line 4 (build codes) you will find boxes under EXHAUST and TAIL PIPE for the LT and RT side part numbers(last 2 or 3 PN digits). If they are both filled in you have dual exhaust. The 73 Charger I had has 000 for the left side under EXHAUST and it was a single exhaust car. Under exhaust mine has 945(LT) and 672(RT) and under tail pipe 02(LT) and 03(RT). Tail pipe part numbers 3466102 and 3466103.
In line 11 (sales codes) you will see under ENGINE ACCESSORIES(sales code N) 2 boxes. One vertically labeled EXHAUST and the other beside it vertically labeled EXHAUST TIPS. Both will have a 4 followed by a dash and have a box below with typed in digits. My 74 has a 1 under EXHAUST for N41 (Dual Exhaust)and a 2 under EXHAUST TIPS for N42 (Chrome Exhaust Tips). The sales car selector book has a statement in the Satellite section under "New for 74", "All V-8 engines with dual exhaust come with bright tips. I don't know if that was also true for Chargers as well.

Just throwing this out there....is it possible that some 360's came with forged crankshafts on 4spd cars? I think I heard something about that a looooong time ago, so I'm not really sure.

I don't believe I've ever heard of nor seen a factory forged crank 360.

Yes 360's were all cast crank engines. Runnin 74 thanks for the input it is appreciated. Problem is I do not have an original car so the build sheet for this particular vehicle that I own would not be if much help. I am putting a 74 SE together with a 360 and am trying to build the car like a car that could have been ordered. Unfortunately there is not a lot of info when it comes to 73-74 b-bodies. This is why I threw this subject out there to learn what I can. I have two 71's and there is plenty of info on them, but even though the two years are "similar" in appearance there are a lot of unseen differences.

Oh yes it is a four speed car. Ta boot

The E58 L code was optional with the A57 Rallye package. Since the Rallye package was not available with the SE model, the SE received the E56 J code engine.

Pretty clear that the car would have a J-code 360, but did this engine have dual exhaust?

My guess, and it's a pure guess, is that you might have been able to order dual exhaust on a J code 360 SE or have it installed by the dealer. There are part numbers for dual exhaust components for 4 door B-bodies and B-body station wagons as well as P, D, and C bodies with engines ranging from 318's to 440's including the 360(and I presume the 2 and 4 bbl 360's although there is no distinction between the two in the parts manual). I also found the "Flange, Exhaust Pipe Ball" listed for "w/360Eng.,w/o/HPerf." and it is the same PN as for the High Performance 360. The only other instances where I see dual exhaust components referred to for 360's other than the high performance 360 are for clamps for the exhaust pipes and tail pipes and tail pipe support hardware. Some of these components are listed separately from the B-body 4 door and station wagon dual exhaust, but not all. It's possible they were only intended for the 4 door and station wagon dual exhaust options. Again the only way to know for sure it was possible would be to find dual exhaust called out in a build sheet for an SE or something in the sales literature indicating dual exhaust could be ordered on an SE.
It looks like from 69CoronetRT's post above that the 4 bbl 360 SE would have come with N95, emission controls, which meant California emissions controls. My Road Runner is a California car and does have the N95 Emission control code on the build sheet. Correct me if I am wrong, but I think sometimes the N95 code also required the N97 noise reduction package which came with tail pipe turn downs instead of chrome tips. My ROAD Runner did come with chrome tips even though it has the N95 emissions code so I do not know if my memory is serving me well.
Finally, if it were me and the car is not original I'd put dual exhaust on it and tell the naysayers that is the way I'd have wanted to be able to order it in the first place.

So if I am understanding you correctly, you have a L code 360 hp with N95? If so that is even more confusing. The info that I have and everything you and everyone else has provided shows J code with N95.

Oh and my mistake you have a road runner and my deliama is for a charger SE. So apparently you could get a L code engine N 95 in California in all dodge and Plymouth b-bodies except a charger SE.

No. According to the model chart in the 74 parts manual the L code 360 (E58) was only available in the Road Runner, Charger, and Charger Coupe. All the other B-bodies got the J(E56) 360 4bbl or K(E57) 360 2bbl.
The Charger SE was available with 318 2bbl. G(E44), 360 4bbl. J(E56), 360. 2bbl. K(E57), 400 4bbl. N(E64), 400 4bbl. P(E68) or 440 4bbl. U(E86) engines.
You will have to look closely at the availability of these engines as some were available in the 49 states and not available in California. For example the 400 4bbl. P(E68) engine was not available in California for Charger SE, Charger, and Charger Coupe, but was available for these models in the 49 states.
Is your SE a California car? Look at the emissions label on the hood. It will be blue if it is a California car and green if it was a 49 state (Federal) car.