For my thesis, I have calculated the constraints for a system using Dirac method of constraint analysis. The problem is I got odd number of second class constraints (!), which gives me unusual numbers of degrees of freedom in phase space. I might have made some mistakes.
Is there any other method beside Dirac, to analyze the constraints of the system?
If the constrained Hamiltonian system has a finite number of real degrees of freedom$^1$, and if all the constraints are regular, then it is mathematically impossible to have an odd number of second-class constraints. (The proof is very similar to the reason why a symplectic manifold or vector space must be even-dimensional.)
Perhaps OP is actually considering a constrained Hamiltonian field theory with an infinite number of degree of freedom and an infinite number of second-class constraints? (Typically this happens because all the fields, say a position field $\phi(\vec{x},t)$ and a momentum field $\pi(\vec{x},t)$, are labeled by a continuous index, namely the space point $\vec{x}$). In that case, it does not make sense to label $\infty$ as an odd number.
Example$^2$: A typical example of a second-class constraints in 1+1 dimension field theory with canonical equal-time Poisson brackets $$\tag{1} \{\phi(x,t),\pi(y,t)\}~=~ \delta(x-y), $$ $$\tag{2} \{\phi(x,t),\phi(y,t)\}~=~0, $$ $$\tag{3} \{\pi(x,t),\pi(y,t)\}~=~0, $$ is
$$\tag{4} \chi(x,t)~:=~\pi(x,t) -\partial_x\phi(x,t). $$
Naively one may think of (4) as a single (i.e. odd!) second-class constraint, but it is really infinitely many second-class constraints labeled by the position $x$. Their equal-time Poisson brackets are
$$\tag{5} \Delta(x,y)~:=~\{\chi(x,t),\chi(y,t)\}~=~ 2 \delta^{\prime}(x-y) $$
with a formal$^3$ inverse
$$\tag{6} \Delta^{-1}(x,y) ~=~ \frac{1}{4}{\rm sgn}(x-y).$$
For another related example of second-class constraints in Hamiltonian field theory, see also e.g. this Phys.SE answer.
$^1$ The definition of degrees of freedom (d.o.f.) is e.g. discussed in this Phys.SE post. (Note that there is also a field-theoretic notion of d.o.f., which is different. E.g. in pure QED in 3+1 dimensions, the photon has 2 physical polarizations, so one would say that pure QED has 2 physical d.o.f., etc. This is not the notion of d.o.f, that I'm considering here. If OP is counting field-theoretic d.o.f., there is no reason to be surprised to meet an odd number, cf. the Example.)
$^2$ This example is sometimes referred to as a chiral/self-dual boson in 1+1 dimensions.
$^3$ One should impose appropriate boundary conditions at $|x| \to \infty$.
There is an elegant constraint quantization method by Jackiw; see http://lanl.arxiv.org/abs/hep-th/9306075
The matrix of the Poisson bracket of the secondary constraints is anti-symmetry, so the number of the secondary constraint is even. If it is odd, there maybe have some new first-class constraints which can be combined by those secondary constraints.
