I would translate "This meat taste of wood" as "Köttet smakar trä" and "This meat tastes like wood" as "Köttet smakar som trä".
For me it is hard to pinpoint the difference between the two in English, but it might be that "tastes of" is more "has the flavour of" and "tastes like" is "has a similar flavour to". So for example, I might say "I think fennel tastes like liquorice" (one flavour reminds me of the other) but "This butter tastes of onion" (perhaps because if has been sitting next to some onion in the fridge). I wondering if the difference is similar in Swedish?
So I tried to 'research' this by googling the phrase "smakar lika", and my conclusion is that all of the results use or imply "som".
Most of the phrases are: Smakar lika gott/bra/illa (Tastes as good/bad)
And this construction is usually used along the lines of "Smakar lika gott som..." (Tastes as good as...)
Another example: Billiga glasögon lika bra som dyra. (Cheap eyeglasses [are] as good as expensive ones.) - this is a headline, so i guess är is omitted just like it would be in English.
One sentence that didn't have "gott/bra/illa": Undrar om det finns billigare korvar som smakar lika som Willys? (Are you wondering if there are cheaper sausages that taste like Willys?)
Another: Vi kommer att jobba ganska lika som vi har gjort. (We are going to work pretty much as we have been.)
One sentence that didn't have "som": Smakar pastan lika gott efter sex veckor? (Does pasta taste as good after six weeks?) But it compares old pasta to itself when fresh, so I think the "som" is implied.
Another: Allt smakar lika. (Everything tastes alike [the same as one another].) Again I think the "som" is implied.
There's also the idiom "lika som bär". (As similar as berries) It means being extremely alike.