My cat also had that "ratty stray" coat. I tried adding oils, using topical oil sprays...but what ended up helping was taking the corn out of her diet and switching her to canned food...I recently had to give her a prescription food for a few weeks that contained corn - the dandruff and scraggly look came back in just a few days, and went away again when I took her off the Rx food. I'll also note that she had the best skin and coat results on a high-fat canned food (I used Wellness). She can't tolerate the high-fat food anymore, so she's getting Innova Light, and though her dryness and dandruff is still gone, she doesn't have the same shine and gloss that the higher-fat food gave.
I'd take a look at your food and see if it has a lot of grains like corn and wheat (even canned foods can have grains in them, and even some expensive foods have a high corn content). Trying either a grain-free food or a food that uses only grains like rice, oats, and barley might help, but you'd need to experiment and see. Canned food might also do a world of good by helping keep the cat better hydrated (cats who eat dry food seldom drink enough to stay well-hydrated). If you're feeding a light or diet food, it may have inadequate fat content to keep the skin healthy.
I'm very leery of cod liver oil because it's very high in vitamins A and D which can be toxic in overdose; you might try fish body oil instead, or even flaxseed oil in a pinch. I know that there are special oil-based coat conditioners they sell that might be more palatable to a cat (often fish oils are flavored for human tastes and cats hate them).
But first, I'd try a food change, cutting out corn and wheat, looking for a higher fat content, and looking for foods with added Essential Fatty Acids. Also, giving at least half of the diet in canned food can do a lot of good. If that doesn't help, then try oil supplements (but be mindful that cod liver oil can have toxic effects in high doses, so you might want to look for fish body oils instead).