Once there's soot on the board and case, all bets are off, and measuring the remains of the resistor probably wont help as odds are, much of the resistive element has been destroyed and redeposited as fine particulates in its general neibourhood!
Find a schematic, either of the exact same model or or a similar one that uses the same value resistors with the same designators (i.e. electrically identical) or a tear-down photo of the same meter at a high enough resolution to read the resistor color codes.
Otherwise it should be possible to trace enough of the circuit to work out the resistor's function, and by circuit analysis, and knowing all the other resistor values, get some idea of its value. Then patch in a resistor substitution box or variable resistor set to the estimated value and check how far off the calibration of affected ranges is. Adjust till all affected ranges are within calibration, then replace with a fixed resistor of the required value. If you cant get all the affected ranges in spec. with a single value of substitute resistor, its likely that there is another fault present.