Serbia, just like the rest of the continent, is metric. Metric system was made official in Kingdom of Serbia in late XIX century.
There are a few obsolete units floating around, for very specific uses. For area of land, everyone knows square meters, ares and hectares, but it's also common to use jutro (morning) of land, and lanac (chain) of land, which may differ in size between regions. I learn their sizes every other year, and keep forgetting them.
Plumbing is expressed in inches - pipes, valves, faucet fittings. However, sewer pipes are metric - sink tube starts at 40mm, then attaches to the main house line at 110mm, then connects to the street via a 160mm one.
Masons may use col (zoll - the German inch), which is not the same as the US inch, the difference being that 1 col = 25 mm, whereas 1"=25,4 mm.
Units may have nicknames - dek is for dekagram, 10g, which is usually applied when measuring food. Many recipes or butcher's customers ask for "20 deka of" something - 200g. Kilogram is almost always a kilo - a 500g loaf of bread is "leba od pola kile" - "bread of half kilo". Drunkards take it as a matter of guild pride to express the amount of liquid in kilos, though not exactly measuring like Russians do - they say "kilo rakije" (a kilo of brandy) meaning one liter. The regular order of "kilo i sifon" (a kilo [of white table wine] and a syphon [bottle of carbonated water with carbon-dioxyde pod in the stopper]) is for connoisseurs of špricer.
Also, generally 1 beer (serbian) is 1,5 beers (american). Standard beer size is 0,5 liters. If you mean american size, then it's a "small beer" (malo pivo).
Spoon sizes: 1 (supena) kašika (i.e. 1 soup spoon) = 1 (table) spoon. There's probably a literalist lurking somewhere who'd say "do they really eat tables with a spoon in the US?". Small spoon, most frequently called coffee spoon (kafena kašika, kašičica za kafu) is smaller than the standard US teaspoon. My guesstimate is that the teaspoon is larger by 50% in volume.