Casimirs are not completely trivial to compute, and somewhat ill defined (if $C_4$ is a quartic casimir and $C_2$ a quadratic, $C_4'=C_4+p*C_2^2+q*C_2$ is another quartic casimir). With generalized Dynkin indices (here $I_2, I_4$) you remove the latter problem (they are fixed) but you must compute even harder.
Since for my special problem probably any Casimir will do, I went the opposite way and defined a quasimir. Instead of a formal definition, an example should make things clear.
Lie algebra is: $B_2$
Heighest weights are: $x,y$
Positive roots are: $x,y,x+y,x+2y$
Set $x\rightarrow{x+1},y\rightarrow{y+1}$ to get: $x+1,y+1,x+y+2,x+2y+3$
Dimension is: $D=(x+1)/1*(y+1)/1*(x+y+2)/2*(x+2y+3)/3$
Quadratic Quasimir is: $Q_2=(x+1)^2-1^2+(y+1)^2-1^2+(x+y+2)^2-2^2+(x+2y+3)^2-3^2$
Quartic Quasimir is: $Q_4=(x+1)^4-1^4+(y+1)^4-1^4+(x+y+2)^4-2^4+(x+2y+3)^4-3^4$
(Depending on definition you have to multiply them by the dimension. Oh, and odd Quasimirs evidently crash, so hands off $A_2,E_6,...$!)
Clearly the computation is child's play now, but of course first someone (and surely not amateur me :-) should a) prove that Quasimirs are Casimirs, b) relate them to those computed from a fairly standard definition (e.g. Wybourne's SCHUR program) and c) relate them to indices. E.g. here is $I_2=Q_2*D/60,I_4=(-12*Q_4+150*Q_2+5*Q_2^2)*D/9$. (Props to Prof. Schellekens for providing me with the raw data.)
So, first things first: Who can prove that a Quasimir is indeed a Casimir?