Is it possible to replace if-else with switch statement using strings as switching values?

Java 7 allows you to switch on Strings.

Your code needs refactoring though, and the question of whether to use switch or enumerations or maps, is something that comes second, I would say.

You have too much duplicated code doing essentially the same thing. I am referring to:

unitValue = Double.parseDouble(tfUnit.getText());
valMeter = unitValue * defined1;
labelDesc.setText("Unit 1");
convert();

Obviously, because you multiply using different factors depending on the unit used, you need a function of unit evaluating to the factor to use. In less mathematical terms, you need something that yields value of either defined1 or defined2 depending on a string supplied. You already have the unit referring to the "name" of your unit in question, you can use it. I call the method returning the factor for factor, taking in a unit name and returning a Number (since it does not follow from your example whether you are multiplying integers or real numbers of some sort). I am also assuming your defined1 and defined2 etc, are variables or literals.

unitValue = Double.parseDouble(tfUnit.getText());
valMeter = unitValue * factor(unit);
labelDesc.setText(unit);
convert();

Number factor(String unitName) {
     switch(unitName) {
         case "Unit 1": return defined1;
         case "Unit 2": return defined2;
         default: throw new Exception("Unknown unit");
     }
}

The method itself is where your "to switch or not to switch" problem creeps in. You are free to use a map if you want:

Map<String, Number> unitNameValueMap = new HashMap<String, Number>();

unitNameValueMap.put("Unit 1", defined1);
unitNameValueMap.put("Unit 2", defined2);

Number factor(String unitName) {
    Number result = unitNameValueMap.get(unitName);
    if(result == null) throw new Exception("Unknown unit");
    return result;
}

Or you can use enumerations:

enum UnitValue {
    UNIT1(defined1), UNIT2(defined2);
    final Number value;
    private UnitValue(Number value) {
        this.value = value;
    }
}

Number factor(String unitName) {
    return Enum.valueOf(UnitValue.class, "UNIT" + Integer.parseInt(unitName.substring(5)).value;
}

You can even switch or use a map inside enumerations, which will give you good code readability as well.

You need to profile your program to see if you need switch-based solution or enum-based one or a map-based one. The way it currently stands and as you can see for yourself, the enum-based solution is a bit messy because of relationship between your unit names, enumeration constants, and their values. If someone can do better with enums, then take their code instead, naturally.

Usually, shortest code is best, as it is easier to read and most often understand. But be careful with maps - they induce more overhead than other solutions, so I for one prefer to use them where I have fewer maps with many keys each, not the other way around.