I will try a protocol using an annealing buffer. You can use a similar protocol for DNA and RNA keeping in mind that the idea is to disrupt any secondary structure within each oligonucleotide.
1. nucleic acids display hyperchromic effect (the increase of absorbance (optical density) when they are single as compared to doubale stranded)
so, use a nanodrop to compare the absorbance of both annealed and single stranded (simple mixture of both oligos).
2. Run a bit of each oligo in isolation and expected annealed oligo on 2% agarose gel with Ethidium bromide. EtBr bind better to dsDNA than ssDNA, so you should see higher intensity if it works...