Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. We present our recent results [PRD106(2022)5,056011] on short-distance expansions of two-, three-, and four-gluon nonlocal condensates up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators. We confirm the results for Operator Product Expansion (OPE) of the two-gluon 0^±+ glueball current correlators and calculate additional contributions coming from dimension-six four-quark condensate and dimension-eight mixed quark-gluon condensates. The OPEs used in QCD sum rules for three-gluon 0^±+ glueballs are revisited up to dimension-six order. QCD sum rules results on masses of C-odd scalar glueballs are briefly reviewed.