Although a common issue, it is not one with a straightforward answer - it will generally require a judgement call as to whether permission is required or not.
To start with, two observations are reasonably certain: the first is that the fair dealing provisions of the Copyright, Designs and Patents Act 1988 (CDPA 1988) in relation to non-commercial research and private study are very unlikely to be relevant, as they do not extend to mutiple copying and making material openly available on the Internet. The second certainty is that there will be no infringement if you have the permission of the quote's copyright owner to relicense that quote.
The position is less clear with regards to the use of the fair dealing provision in relation to criticism and review. Where the excert has been previously published, is being used for the purposes of criticism and/or review, s.30 of the CDPA 1988 may permit the inclusion of the quote (accompanied by acknowledgement of source). However, a judgement has to be made as to whether the activity is truly criticism and/or review (rather than, say informing and illustrating), and whether the use is fair. The judgement of fairness might include factors such as the extent of the quote, and its commercial value (or potential value).
In some situations, it may be possible to argue that the owner of copyright in the work from which the quote originates can be deemed to give an implied licence to use a quote. However, it will be up to the person using the quote to prove that this is the case. Where the quote has been published in an academic context where quotes are regularly and commonly included in others' work, it may be possible to argue an implied licence. However, where the inclusion is for criticism or review, the fair dealing right described above may be more certain.
As illustrations of approach, the University of Cambridge refers to this issue at: http://www.caret.cam.ac.uk/copyright/Page180.html#Topic125, or Brunel University at: http://www.brunel.ac.uk/life/study/library/sylat/copyright/fairdealing.
Where certainty is sought, this will entail seeking the permission of the rightsholder (providing the copyright period has not expired, you are not the copyright owner, and you currently do not have permission to do what you propose. The SHERPA ROMEO project website has extensive information on publisher’s policies which might be helpful in identifying the particular journal and its publisher’s terms. This can be accessed at: http://www.sherpa.ac.uk/romeo/.
In conclusion, various rights may exist in journal articles and their contents. In order to make quotes from these articles available in an online OER context you will need either to make a judgement as to whether the fair dealing provision in respect to criticism and review might apply, or whether implied licence can be assumed. If neither of these conditions apply, permission needs to be sought from the copyright owner for inclusion of the quote.