The following are generally accepted as OE pre-modals: cann 'know, know how to' (> can); dearr 'dare' (> dare); mæg 'have power, be allowed' (> may); mot 'must' (past moste > must); sceal 'shall, must' (> shall); þearf 'need to' (now obsolete); and wile 'wish, intend, will' (> will). The inventory for ME remains much the same, merely adding mun 'must' (Mitchell 1992, Warner 1993, Denison 1993). As most of the literature focuses on can, may, must, shall, and will, I shall concern myself most with these.
All the pre-modals were irregular from the outset, belonging as they did (except for wile) to the preterite-present inflectional class. The present forms of these verbs were derived historically from strong preterites, and new past forms were created, by analogy, on an irregular stem. They had more-or-less fully realized paradigms in at least the indicative, where they maintained the major category distinctions of person and number. They were irregular in that they did not undergo 3rd person singular agreement, nor did they have regular agreement in the preterite singular. They did, however, have a distinct 2nd person singular form. Most of these inflections were lost in the sixteenth century along with those of other verbs. Table 1.1, adapted from Denison (1993, p.296), illustrates the major differences in the paradigms of the preterite-presents and wile on the one hand, and normal verbs on the other.
The pre-modals were not the only preterite-present verbs. During ME, however, those which were not pre-modals tended to either join more regular inflectional classes or drop from the language altogether. Plank (p.312) notes that most of these were synonyms for the more common pre-modals, citing witan (near-synonym of cunnan), unnan (root meanings similar to other modals), *dugan (similar to magan), and several others.
Non-finite forms were also irregular. Some pre-modals never had any to begin with, while others innovated forms in the ME period. Further, where non-finite forms are used, they rarely have anything but notional meaning, i.e. they cannot be translated with a modern modal. Infinitives can be found in Visser for can and may. At least two different infinitives existed for the former: to conne occurred sporadically in ME, while infinitive con was fairly frequent. The infinitive mowen, mown, mowe, mow was obsolete by the fourteenth century, though the "double modal" construction of the type shall may was common in ME. It is likely that this was an innovation of that period (see de la Cruz 1993 for discussion).
Both present and past participles are recorded for not only can and may, but also for will. These forms were common for can from the fourteenth century on, while mowing/mowende was frequently found in both OE and ME. Most of these forms became obsolete, while willing underwent a semantic shift.
Warner provides a handy table to summarize the non-finite forms for the other pre-modals in both OE and ME (1993, p.145), which I have adapted (Table 1.2).