By the creative use of various footnotes in T.B. Pugh's Henry V and the Southampton Plot I have calculated that Edmund of Langley's income from land and annuities amounted to £2070 a year. Almost £1,100 of this was made of of annuities, and so it follows as night follows day that his income from land was less than £1,000. Edmund's widow Joan (or Joanne) Holland was entitled to a one third share for life.
Duke Edward's inheritance was therefore roughly £1,366, with maybe £600 from land. OK, he had what was left of the additional lands given him by Richard II, plus Philippa's relatively modest dower rights, but, given that for much of Henry IV's reign annuities were about as valuable as Bradford and Bingley shares in 2009, this was not much to run a dukedom on. It's not hard to see why debts of ten grand from his time in Gascony, and further debts run up while fighting Henry's battles in Wales would have given him serious problems.
Edward received some wages in addition. For example he had twelve pence a day as Master of Hart Hounds and a salary of £200 a year as a member of Henry's Council. However, this would have been a lot less in total than he received from the juicy offices he held under Richard II, and I expect the wages were often paid in arrears, given the state of Henry's finances.
To give some comparisons, the Mortimer inheritance in England and Wales was conservatively estimated at being worth £3,400 in 1398, while circa 1415 the Despenser inheritance, despite all it had suffered from forfeitures and the ravages of Owain Glyn Dwr's friends, was still reckoned to be worth £1,500. In 1391 the duchy of Lancaster was worth about £10,000, while Pugh estimates that Gaunt's total income at the end of his life was more like £20,000.
Despite grabbing what he could from the Despenser wardship Edward was still reduced to mortgaging some of his lands to pay the debts he ran up in the Welsh wars, and in 1404 was wandering around borrowing from anyone he could, including the Abbot of Glastonbury. This was probably one of his motives for seeking to overthrow Henry in 1405, and, frankly, he had more cause to complain on the effect of government policy on his finances than Thomas of Woodstock had in the 1390s.
Although Henry's finances improved in the later part of his reign and Edward (presumably) saw more in the way of hard cash, he still ended up selling (in 1412) the Lordship of Tyndale, together with the reversion of Joanne's one third share to Sir Thomas Grey for £500. This may have had something to do with the proposed marriage of Richard of Conisbrough's daughter, Isabel, to Grey's son, but generally speaking the sale of inherited land was something that was done only as a last resort.