You can pick wild berries and mushrooms for example in Nuuksio National Park. It's accessible by bus from Espoo. Picking berries and mushrooms is allowed in the park, and it's free of charge.
http://www.nationalparks.fi/en/nuuksionp
Bilberries and lingonberries are easy to recognize and pick. Biberry season is from mid-July to early September, lingonberry season is from September to October. Be prepared with a bucket / bag and a "marjanpoimuri" if you intend to pick a lot. It costs around 5 € depending on the model.
https://www.prisma.fi/fi/prisma/marjukk ... imuri-ergo
If you pick with a poimuri you end up with a lot of leaves and needles etc. in your bucket. You can remove the trash by hand or by using a "marjanpuhdistin".
http://www.plastex.fi/marjanpuhdistin-3 ... ainen.html
There's a strawberry farm in Espoo:
http://www.kartanonmarja.fi/
Apparently you must be prepared to pick at least 2 kg, or you can buy berries they have already picked. Strawberry seasons starts in July. I'm not sure about the price. Alternatively you can expect to buy a 5 kg box of fresh strawberries from almost any larger supermarket during the season. They cost 20-30 € on a good strawberry year (last year was a bad one).
If you intend to pick berries for freezing, you'll also need sugar, as well as plastic bags or boxes for storing in the freezer.
Information on Finnish berries:
http://www.dlc.fi/~marianna/gourmet/i_berry.htm
Information on Finnish musrooms:
http://www.dlc.fi/~marianna/gourmet/i_mushro.htm
When it comes to mushrooms, only pick the ones you recognize to be safe to eat!
