Could well be a Phytoseiid but unfortunately, it's almost impossible to confirm, even to family, without it mounted on a slide.
This free online key will give you an idea what kind of thing your looking for http://itp.lucidcentral.org/id/mites/invasive_mite/Invasive_Mite_Identification/key/Mesostigmata/Media/Html/Home_Mesostigmata_in_Quarantine.html
On strawberries you can find a lot of species of predatory mite. it could be A.swirskii, N.californicus, N.cucumeris, A.limonicus, and others. The best is to mount on a slide and send it to Biobest in Belgium, Koppert in Netherlands, University of Wageningen NL or Mr Kreiter from SupAgro Montpellier, France.
Can you post some pictures of slides? Otherwise, you can indeed send some mites in alcohol (or alive) and we can identify it for you. Let me know if I can be of any help.
Strawberries have a wide infestation with Tetranychus urticae, so that the predatory mites which may found like Phytoseiids, Phytoseiullus persimilis, Typhlodromips swirskii, Neoseiulus californicus and N. barkeri. These species are the most commercially used to control red spider mite.
Pictures are not so clear to me, but I handled phytoseiid mites before, and I could guess this are phytoseiids
To be more accurate, try to mount it on a slide, the tibia I has a chaetotaxa of 2/4/2 (Ref.: A Manual of Acarology, 2nd Ed. 2009) if you found that equation it is a phytoseiid and if not you can send them to Dr. A. K. NASR, a professional mesostegmata taxonomist (National Research Centre, El-Bohouth St., 12622 Dokki, Giza, Egypt. +20-01001965573; [email protected]).
Dr. F.M. MOMEN, she consider herself not a Phytoseiid taxonomist but a biologist. I truly knew that she could discriminate between life material according to their biology and feeding preference. (National Research Centre, El-Bohouth St., 12622 Dokki, Giza, Egypt. +20-01227534060. [email protected]).
Also, Dr. Ukermann in South Africa could help you well
Although the photos are not clear as well, but I agree with Peterson R. Demite. It seems to be a species of Blattisociidae, not a phytoseiid mite. Better photos, especially from slides, are helpful for exact identification even for family level.