Ghost Hound revolves around mystery which means canon likes to be ambiguous on Miyako and her powers. Here I'm going to take what I can from canon to explain them and make some cross-canon compatibility.
Miyako can see and be possessed by spirits. However, she's a little tricky in her ability to see them. Miyako can not distinguish them that well, apparently. Canon shows them clearly, but she ends up having to squint and describing Tarou's OBE by what color he is rather than his form. Miyako doesn't see just spirits in color though; she sees everything with a color. Ironically, she's the daughter of a Shinto shrine which believes that everything has a living spirit in it. So, when she chooses to Miyako can probably trip out very well just by standing and staring at anything.
As for how strong she is, Miyako is touted in canon as having exceptional power. We aren't told what Makoto's grandmother did in her heyday, but it's not hard to believe that Miyako surpasses her. Spirits that are thousands of years old are able to enter her, translating their powers in her easily. Miyako can also sense spirits from very far away, getting effectively pinged by the boys miles off when they enter Kakuriyo. However, Miyako lacks any control. She has massive raw power, but has no guidance on how to control it for a number of reasons.
Within camp, Miyako has been training under Anna to control her power. So far what she's been able to perform at a very slow and steady rate is shielding herself from spirits, so they can't get close enough to cause trouble for her. At the moment, she can shield a small area around her from weak spirits while focusing. After a very long time, she'll likely be able to do large-scale, thick-as-all shields. Miyako will eventually pick up the ability to push spirits out once they've already entered too. It will just take awhile for the sake of antics and Miyako's play longevity. Miyako's ability to see spirits more clearly and sense them is also improving the process as she works on her spiritual sensitivity.
For the record, she will not be pulling any Mankin antics. So, no spirit partner or doing oversouls for her. She might move on to gain some itako mastery from Anna, but Miyako has no interest in it at the moment, so it's null and void for now.
While I'm canon reviewing, Tarou and Mizuka were abducted on September 22, 1996.* They were discovered four days later. Everyone knows the rest. Hideo Ogami committed suicide on October 2, 1996.
GH CAST - I'm still fussing with Miyako's birthday. Who wants to vote on the creepiest best date?
* Do not rely on Wiki. Sorry, Tarou.