“death's dateless night”
'Dateless' means without a fixed end-date, unlimited, perpetual. A lease or a court term has a date of expiry; death's night has none. The legal idiom of the poem makes 'dateless' especially precise: unlike a financial debt with a due date, death has no term and cannot be redeemed.
“love's long since cancell'd woe”
'Cancelled' is a legal and financial term: to cancel a bond or debt was to cross it out or void it, marking the obligation discharged. The speaker thought a past grief had been settled — cancelled like a paid debt — but finds he is weeping it 'afresh,' as if the cancellation never happened.
“expense of many a vanish'd sight”
'Expense' here means both expenditure (the cost paid in tears and grief) and loss (the things spent and gone). 'Vanish'd sight' means people or scenes once seen but now disappeared — things the eyes once held that are no longer visible. The line mourns not just dead friends but any cherished experience now lost.
“heavily from woe to woe tell o'er The sad account of fore-bemoaned moan”
'Tell o'er' means to count through item by item, as an accountant goes through the entries of a ledger. 'Fore-bemoaned moan' means grief already mourned before — sorrow that has already been lamented and yet is being lamented again. The speaker is doing double accounting: paying a bill he has already paid.