In this work, we perform coarse-grained (CG) and atomistic simulations to study the effects of polymer conjugation on hybridization/melting thermodynamics of oligonucleic acids (ONAs). We present coarse-grained Langevin molecular dynamics simulations (CG-NVT) to assess the effects of the polymer flexibility, length, and architecture on hybridization/melting of ONAs with different ONA duplex sequences, backbone chemistry, and duplex concentration. In these CG-NVT simulations, we use our recently developed CG model of ONAs in implicit solvent, and treat the conjugated polymer as a CG chain with purely repulsive Weeks Chandler Andersen interactions with all other species in the system. We find that 8-100-mer linear polymer conjugation destabilizes 8-mer ONA duplexes with weaker Watson Crick hydrogen bonding (WC H-bonding) interactions at low duplex concentrations, while the same polymer conjugation has an insignificant impact on 8-mer ONA duplexes with stronger WC H-bonding. To ensure the configurational space is sampled properly in the CG-NVT simulations, we also perform CG well-tempered metadynamics simulations (CG-NVT-MetaD) and analyze the free energy landscape of ONA hybridization for a select few systems. We demonstrate that CG-NVT-MetaD simulation results are consistent with the CG-NVT simulations for the studied systems. To examine the limitations of coarse-graining in capturing ONA-polymer interactions, we perform atomistic parallel tempering metadynamics simulations at well-tempered ensemble (AA-MetaD) for a 4-mer DNA in explicit water with and without conjugation to 8-mer poly(ethylene glycol) (PEG). AA-MetaD simulations also show that, for a short DNA duplex at T = 300 K, a condition where the DNA duplex is unstable, conjugation with PEG further destabilizes DNA duplex. We conclude with a comparison of results from these three different types of simulations and discuss their limitations and strengths.