There is no absolute consensus for reporting abbreviations for splitting patterns. Even Magnetic Resonance in Chemistry, a journal that I generally take as the best guide for reporting NMR data, does not have recommended abbreviations for multiplicities above quartets. Further, there are general inconsistencies in reporting formats within this journal, with abbreviations such as s, sept, spt being used for septet. Additionally, the actual term used to describe the splitting varies. For instance, both pentet and quintet are commonly used to describe a 1:4:6:4:1 splitting.
What is consistent, however, is that the abbreviations are defined within the paper.
Commonly used terms and abbreviations that I have come across include:
pentet (p, pent, pnt, pentet) or quintet (q, quint, qui, qnt, quintet)
sextet (sext, sxt, sextet)
setpet (s, sept, spt, septet) or heptet (hept, hpt, heptet)
octet (oct, octet)
nonet (non, nonet)
While splittings of higher multiplicity are less common within mainstream CHN organic molecules (septet for isopropyl substituents are a common exception, and 'apparent' splittings are excluded), they are more common with heteronuclear substitutions and organometallic systems, where spin numbers greater than 1/2 are frequently encountered. Reporting 'apparent' splittings of, say, (CH3)2CHCH2R as a nonet (where Jab ~ Jac) is not strictly correct according to the 2nI+1 rule, although in non-NMR journals still occurs, and is certainly taught at undergraduate NMR level.
As for reporting multiple couplings (doublet of septets, for example), again there is no strict rule to adhere to, although the commonly adopted practice is to report the larger coupling first. So, a doublet coupling of 10Hz and septet coupling of 2Hz would be a doublet of septets. If it were doublet (2Hz) and septet (10Hz), one would report a septet of doublets.