You are in a bad spot as there is not a good upgrade path. To get into a more modern CPU, you will need a new CPU/Mobo/RAM. You could go with a 4th gen Intel CPU that would be a bump. All you would need is a new mobo and CPU, but they hold their value pretty well and I think would be better off getting a 2600 and b450 mobo.
If you can find a good deal on a used 4790k and mobo combo it may be worth it.
Here would be a decent 2600 build. It is a really good CPU, but may be over budget.
PCPartPicker part list:
https://pcpartpicker.com/list/pngdxG
Price breakdown by merchant: https://pcpartpicker.com/list/pngdxG/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor ($159.89 @ OutletPC)
Motherboard: Gigabyte - B450M DS3H Micro ATX AM4 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-3000 Memory ($79.99 @ Newegg)
Total: $309.77
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-29 14:58 EDT-0400
Here you could save a little money with a lesser CPU, but still better than your 8320. Either way, you gotta have RAM.
PCPartPicker part list:
https://pcpartpicker.com/list/fQYPKB
Price breakdown by merchant: https://pcpartpicker.com/list/fQYPKB/by_merchant/
CPU: AMD - Ryzen 3 2200G 3.5GHz Quad-Core Processor ($98.49 @ SuperBiiz)
Motherboard: Gigabyte - B450M DS3H Micro ATX AM4 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-3000 Memory ($79.99 @ Newegg)
Total: $248.37
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-29 14:59 EDT-0400