The development, integration, and maintenance of geospatial databases rely heavily on efficient and accurate matching procedures of Geospatial Entity Resolution (ER). While resolution of points-of-interest (POIs) has been widely addressed, resolution of entities with diverse geometries has been largely overlooked. This is partly due to the lack of a uniform technique for embedding heterogeneous geometries seamlessly into a neural network framework. Existing neural approaches simplify complex geometries to a single point, resulting in significant loss of spatial information. To address this limitation, we propose Omni, a geospatial ER model featuring an omni-geometry encoder. This encoder is capable of embedding point, line, polyline, polygon, and multi-polygon geometries, enabling the model to capture the complex geospatial intricacies of the places being compared. Furthermore, Omni leverages transformer-based pre-trained language models over individual textual attributes of place records in an Attribute Affinity mechanism. The model is rigorously tested on existing point-only datasets and a new diverse-geometry geospatial ER dataset. Omni produces up to 12% (F1) improvement over existing methods. Furthermore, we test the potential of Large Language Models (LLMs) to conduct geospatial ER, experimenting with prompting strategies and learning scenarios, comparing the results of pre-trained language model-based methods with LLMs. Results indicate that LLMs show competitive results.